Why is an angle of attack indicator not commonly included on small airplanes? Is it too expensive?
Historical inertia, mainly. AoA indicators aren't too terribly expensive to install anymore, but they were until very recently. We are now in a period where AoA indicators are fairly inexpensive and often standard in new aircraft, but most general aviation pilots are flying older aircraft and are used to flying without them.
General aviation is slow to change. Give it a few years or decades and I'm sure you'll start seeing them more and more.
One reason is just that it is hard to build as a console instrument for light aircraft. Just having an indicator on the side is easy, but having it show up in instrument cluster requires measuring an angle and then transmitting it to a dial. This is not straightforward in a repeatable way (especially where the vane part has to be exposed to weather).
The classic six pack instrument cluster is classic in part because they are instruments easy to mass produce and maintain driven by pressure alone, or using DC power of indifferent quality.
Measuring angle and remotely displaying it was traditionally done using synchros which crucially use AC power of steady frequency, normally 400hz. They were a widely used, highly reliable and well understood method of making servo systems including those on larger aircraft needing power assisted controls/autopilots. So if an aircraft already has a reliable 400hz power system for existing systems adding angle of attack sensor just means adding another angle transmitter of a type probably already widely used in the airframe, along with an repeater in the cockpit, total weight less than a kilogram and using cheap (for aviation) parts.
If the aircraft does not have a 400hz power system then adding an synchro based sensor becomes a complex power generation problem.
This couples angle of attack sensors to aircraft with larger and more complex electrical systems, which generally does not include light aircraft.
Now with compact electronic angle sensors it becomes simpler to add an angle of attack sensor for aircraft with DC only electrical systems, but as per the existing answers the baked in inertia from the earlier era still exists.
Chris's answer is spot on, but I'll add a bit.
Retro-fitting is expensive, and getting airframes included in a cert (if the airframe is no longer in production) is a calculated risk. AOA sensors are becoming standard on some new airframes but most of the GA fleet is made of of old aircraft that change hands on the used market; many of these aircraft are out of production so building and certifying new systems for them is a calculated risk/cost for manufacturers.
You are liable to find AOA sensors on new airframes like new 172's but until the FAA mandates them, adding a luxury sensor to a dated airframe is going to be a cost/benefit choice that many are not going to easily make, considering the cost of required upgrades the GA fleet has made in the last decade or so. Everyone was hit with the ADS-B out upgrade, it's getting to the point where practically flying IFR requires an IFR GPS to really make use of the NAS, and those installs don't come cheap. Even though AOA sensors are cheaper than ever, they are not required, so you are unlikely to find them widely installed.
One reason is that most of the light airplanes already have one of sorts in the stall warning.
The stall warning sensor is basically an angle of attack instrument of sorts, although with only two values. As example the Piper Cherokees has a small tab on the wing that reacts when the air starts to move "upwards. Older Cessna 172-s has a device that makes a sound when airflow changes around the wing.
--- added Most General Aviation aeroplanes, say PA28 or C172, are made to have docile flight charecteristics. In effect this means that they will behave in a predictable and simple way even when mishandled a bit allowing the pilot plenty of time to return to safer flight conditions. In that situation an AoA meter does not really add very much to the pilot. In contrast, high-performance aircraft may have quite "angry" responses when flown. They might, perhaps with very little warning, clip towards one side whan AoA becomes to high, or perhaps enter a height eating stall. Close to ground this can be fatal. In those aircraft an AoA indication can be a life saver. I guess that most jet fighters landing on aircraft carriers comes into this category.
In some limited cases an AoA meter may be helpful in cruise allowing the pilot to optimize for lower fuel consumption. The reason is that some aircraft tend to "hang on the step" with non-optimized performance unless carefully beeing convinced otherwise. Again, the typical General Aviation aircraft does not really have this behaviour.
AoA instruments can malfunction exactly as all other instruments. The worst case would be if the instrument shows wrong values in a way that makes the pilot make otherwise unnessary mistakes. And this has actually happened in some fatal crashes (although several other factors where in effect as well).
In effect -- why add one more instrument that can malfunction when it really adds nothing in safety or performance for a typical GA airplane.