10 degree flaps increase our lift, reduce stall speed, reduce ground roll. Seems like all advantages with no disadvantages. So why does the Cessna 172 POH say normal take off is 0-10 degree flaps? Why not always use 10 degree?
Flaps out will reduce the ground run, but you're forgetting that they also increase drag. This is why you don't climb all the way to cruise altitude with flap extended. A 172 will climb better without flaps.
With a take-off, you have to consider both the ground run and initial climb. After all, the take-off distance required is defined as the distance required to climb to screen height (50ft in Australia, sorry if the US is different). The aircraft also has to meet a legal minimum climb gradient to that height.
Without looking at the data, it is possible that in certain conditions, taking off with flaps 10 will get you off the ground quicker, but will actually take longer to reach 50ft compared to a takeoff with no flaps. In any case, retracting flaps in a busy time after takeoff is a potential hazard, and in a training aircraft like the 172 simple procedures are best.
The issue is how one wants to optimize their flight operations. Generally the emphasis is on time to climb, however for some operations, such as out of standing snow, slush, mud and grass, and in the case of seaplanes, glassy water, the preferred optimization may be to minimize ground roll, rolling drag, tire wear or other factors. I teach both techniques, so that the pilot understands the choices he has, and the ways he can accomplish things.
Concerns about "stalling out" after rotation, are an issue of proficiency. Correct instruction and recurrent practice help address proficiency.
Probably 2/3 of my flight review students rarely use flaps in a C172 for take off, and generally only when doing soft field or turf takeoffs. So with those students, we tend to review takeoffs with flaps, and how they may be operationally effective in situations other than just a turf or dirt field. For those more fluent in flapped takeoffs, there are other things we might spend time on.
From a personal perspective, I probably use 10 deg flaps on a C172 95% of the time, because I like to minimize wear on my tires.
With 10 degrees of flaps and the trim wheel in the "take-off position" my C-172 will rotate without any back pressure on the yoke. You have to apply forward pressure to keep the speed above 62 knots. A flight instructor a few years ago during a flight review suggested I always use 10 degrees of flaps during take-off. After using this method for a few months, I concluded that using 10 degrees introduced a new hazard. A stall during take-off was more likely. I went back to 0 degrees flaps.
There’s nothing saying that you can’t. And for a performance takeoff like a short field take off, you will use 10° of flap. It’s just in general conditions combined with the fact of the Cessna 172 only has a takeoff roll around 1000 feet or so at sea level conditions, there’s not much need to use flaps. You can use up to 10° of flaps if desired. But generally most pilots don’t .