You can’t rely on it if you don’t know the acceleration as a function of time.
We already have a general formula.
Any general result you get will not, and cannot, be different.
Who said it’s rare?
We didn’t use constant acceleration to derive KE.
We did use constant acceleration because those problems were easiest to solve, which is what you do for introductory physics. Later, you spend a lot of time learning how to solve the non-trivial cases
No it's not. g is only approximately constant, and only near the surface of the earth (or other large body). Gravitational force varies as 1/r^2.
And freefall is only approximately a constant acceleration if you ignore air resistance.
Homework problems are not so uncommon, because we simplify them. Real-world problems, not so much.
This makes no sense.
There is a connection in your mind, but that doesn’t mean there’s any legitimate physics there.