Why can we not use full throttle in a C172 when cruising at lower altitudes?

I agree with the above answers in terms of the limitations related to engine. However I wanted to also add that it could be possible that going full throttle at a low altitude would cause the aircraft to go out of its structural flight envelope as well. So as much as being an engine related issue, it could also be due to structural considerations of the airplane.

These engines are not designed to run at maximum horsepower output all the time with a lean mixture. They are designed to cruise at 50-75% of their rated max power, and deal with that level of internal heat and friction over the long term. Even this is fairly hard compared to a car that runs at perhaps 20% of rated power when cruising at 60 mph.

Running them wide open means maximum heat, maximum wear, for not much benefit considering the power required to go faster is nearly the cube of the speed increase. You must run with the mixture full rich to keep the engine cool at all, and fuel burn is a lot higher because you are dumping unburned fuel used for cooling at full power out the exhaust. It's not worth it in other words, unless you are racing, so the concept of cruising at not more than 3/4 of rated max power is a very old convention in piston engines, and mixture leaning shouldn't really be done above that.

You can run one of these engines at full throttle with a rich mixture with the RPM near red line all the time if you want, but only if you don't mind paying for the 20 thousand dollar premature overhaul from flogging the poor engine like a mule (the exhaust valves will hate you for all eternity).

It's pretty much the same thing as hooking up a big heavy trailer to your car, that required foot on the floor all the time just to stay at highway speed. How many miles do you think that car's engine would last?(Although the Lycoming being run that hard will still probably outlast the car engine in the same shoes.)

However, when you go up, by the time you get to 8000ft, 75% of maximum output is all that is available with wide open throttle (WOT) in the thin air, so 75% cruise, normal operation, requires WOT and no harm is done. And as you go up further, you find you can't even get 50% with WOT and pretty soon you're at your service ceiling.

Most Cessna 172s have fixed-pitch propellers. Designing a fixed-pitch prop always requires making some compromise between climb performance and cruise performance. Typically this means that at low altitude in horizontal flight, at full throttle the engine would exceed redline RPM, so you have to throttle back. At higher altitude the engine produces less power at a given RPM, so it isn't a problem there. It's possible to use a "cruise prop" that has a coarser pitch and allows full power (or closer to full power) in low altitude cruise, but this comes at the expense of not making full redline RPM at the start of the takeoff roll, and therefore lower acceleration and longer takeoff runs.

Variable-pitch propellers (of which "constant-speed" propellers are a subset) avoid this dilemma, though they have their own downsides such as increased complexity and a bunch of extra weight right on the nose where you don't want it.