When I land the airplane (Cessna 172, 182, 152) I notice that I come in pretty far above glide slope (four white lights on the PAPI). I pick an aiming spot on the runway (like the second center line stripe) and maintain my approach airspeed while flying towards that point. I'm able to reach that aiming point with quite good accuracy and land the plane smoothly and softly, but I'm above glide slope for most of the approach, and then on short final the white lights start to turn red. Clearly my approach is steeper than the usual 3 degree glide slope. I thought that's what flaps were for - to allow for a steeper approach. Am I doing this wrong? Should I focus on staying on glide slope, or should I focus on my aiming point? I've had several flight instructors and most of them have never said anything about this. I kinda like being a little higher, and approaching exactly on glide slope usually means I have to add power on short final because I start getting too low.
It is more important that your approach is stabilized and safe than you are strictly on slope (i.e. two red/two white). But let's discuss a few things before extending this answer.
ATC is not terribly concerned with where exactly you touch down (especially in a light aircraft) so long as you don't run off the end of the runway. When cleared to land the whole length of the runway is yours to work with:
If receiving “cleared to land” instructions from ATC, you are authorized to use the entire landing length of the runway and should disregard any LAHSO holding position markings located on the runway. If you receive and accept LAHSO instructions, you must stop short of the intersecting runway prior to the LAHSO signs and markings.
Different runways will call for different touchdown situations which is why it's important in preflight to understand what your landing distance and roll out will be.
In any aircraft you fly you should be proficient (or learning to be proficient) in various landing techniques than includes standard approaches as well as no flap approaches and short field landing maneuvers. If you have all these things in your toolkit you will be fine. If you are proficient in an aircraft you should be able to put it down on the numbers or the 1000 foot markers or any other spot your instructor asks you to demonstrate so long as there is sufficient distance to roll out and stop. You should focus on being able to deliberately put the aircraft down on a spot of your choosing rather than thinking of it in terms of "i always end up touching down on the mid point of the runway" as the latter statement means a very different thing on a 2000 ft runway than it does on a 10,000ft runway. This can generally be controlled with small pitch and power changes on final.
Generally speaking you should fly the glide path if it is available to you as this will guarantee obstacle clearance and keep you safe. While it is never bad to be a bit above glide path (three white, one red) it can be problematic to be very high (all white). The issue with 4 white lights on a PAPI is there is no further indication of how far above glide path you actually are. Making the assumption that you are anywhere near the glide path if you see 4 white lights is dangerous and can lead to a fast, unstable, slam dunk approach. Slope adjustments can be a bit delayed on approach and a power increase will generally bring you back up to slope if you are low while chopping the power will bring you down to slope but remember it will take some time to settle in so you need to think ahead of the airplane.
If you put it all together you will see that staying on slope brings you down to the 1000 'footers, keeps you clear of obstacles, and allows you to make small final adjustments to control your touch down if you want to land a bit short or a bit long.
It is not a question of focusing on one OR the other but focusing on both and realizing how they play together. If you come in on slope you can make small power changes to adjust your aiming point and suit your desired maneuver.
Stabilized Approach Concept
A stabilized approach is one in which the pilot establishes and maintains a constant angle glide path towards a predetermined point on the landing runway. It is based on the pilot’s judgment of certain visual clues and depends on the maintenance of a constant final descent airspeed and configuration.
An airplane descending on final approach at a constant rate and airspeed is traveling in a straight line toward a spot on the ground ahead. This spot is not the spot on which the airplane touches down because some float occurs during the round out (flare). [Figure 8-9] Neither is it the spot toward which the airplane’s nose is pointed because the airplane is flying at a fairly high AOA, and the component of lift exerted parallel to the Earth’s surface by the wings tends to carry the airplane forward horizontally.
To address some points of your directly:
I thought that's what flaps were for - to allow for a steeper approach.
Flaps allow you to fly a steeper decent angle at a given airspeed, this is not a blanket security measure to fly arbitrarily steep approaches at 80Kts in a 172. They also help you to generate more lift at a given airspeed so you can fly a standard approach at a slower than normal speed (think short field landing).
...and approaching exactly on glide slope usually means I have to add power on short final because I start getting too low.
If you are on glide slope on short final you are not too low (thats the point of a glide slope). If you are high for most of the approach, cross the slope, then find your self sinking below slope your approach is not stabilized and you are likely coming in hot then cutting power and diving for the runway.
I kinda like being a little higher
While there is no strict regulation on flying above glide slope flying arbitrarily high is typically an indication of an unstable approach that will result in a slam dunk dive final. The glide slope exists for many reasons and should be followed for those reasons.
If you are student pilot (you dont mention here) work on flying stable, on slope approaches. If you already have your ticket I would start some Instrument training and understand what its like to fly the slope in the soup (or foggles) and how being high can be a real issue when you break out, it might help put it all into perspective.
Remember, glidepath guidance has its apex or ending point centered on the official precision landing markings (what most people call the thousand footers). This is officially called the aimpoint or aiming point. Large aircraft do not have much float when flaring. They both aim and touch down near the same point. Walk out to a point abeam the thousand footers. You will see the vertical guidance equipment located next to the runway, beside the thousand footer markings.
Your little Cessna floats so much that your aiming point and your touchdown point are not coincident. If you want to land on the thousand footers, you have to aim at the first touchdown marking (the five hundred footers). If you follow the VASI, PAPI, ILS or RNAV glideslope/glidepath all the way down to the ground, you will float past the thousand footers as soon as you enter ground effect.
You are supposed to stay above the glideslope to provide for obstacle clearance all the way to a point where landing is assured. This is usually either the runway lead up lights (MALSR, ALSF, etc) or the runway threshold. Most instrument approaches will include a Threshold Crossing Height on their charts.
During training, focus on landing based on sight picture alone. You will need that when landing on runways without vertical guidance. There are a lot of them. You will also need that skill when doing actual, non-simulated short field and soft field landings. On a real short field landing with a 50 foot obstacle, your aiming point Will be well before the Arrival End of the Runway. It may even be before any concrete starts.
Flaps generate more lift at the expense of more drag. Their primary purpose is to allow you to fly slower, with the side effect of letting you descend more steeply without gaining speed.
Your default should always be to use the VSGI when one is available, and to try to stay on glide slope, unless you are deliberately doing something unusual like a short field landing, power off 180, etc. This will build good habits and control that is critical when you advance to instrument flying and larger aircraft.
I can't say for certain why your instructors haven't commented on your steep approaches; maybe they just didn't care since it was "working" for you. I'm sure they would have said something if you were consistently below glide slope, though.
If you're flying your pattern with the appropriate flap settings, speeds and distance from the field, you shouldn't have much trouble staying on glide path. Without seeing you firsthand, I'd guess that you're too high or too fast, which makes you reduce power too much and dive toward the runway, and then on short final you need to add more power to shallow your dive. If you were on glide path to begin with, you would be reducing power on short final since you're about to enter ground effect.
Regarding the 172, and any other single engine aircraft, a better question might be:
what if I lose my engine on final approach?
We can start by looking at the angle and rate of descent with no power at Vbg, around 65 knots. With an 8:1 glide ratio, no flaps, the angle of descent is:
arc sine (1/8) = 7.2 degrees
rate of descent = 65 knots × 1/8 × 6076 feet/nmile ÷ 60 minutes/hr = 823 feet/minute
We can see that, if local regulations allowed, a higher angle of approach would be the safer way to assure reaching the runway, particularly if there were obstacles such as buildings or power lines in the flight path.
At a low idle:
thrust is proportional to rpm$^2$
thrust required for level flight @ 65 knots= Weight × .125 = around 300 lbs or roughly 1700 rpm
900$^2$/1700$^2$ × 300 lbs = 84 lbs of thrust
Angle of descent at idle = 7.2 × (300-84)/300 = around 5.2 degrees
This is all without flaps, which will steepen angle of descent.
...kinda like being higher
This is a great idea. 3 degrees approach is more for the faster, heavier, multiengine aircraft. More power must be added for a lower angle of descent. Always leave a way to glide a single engine home if you can.