Yeah changing one tyre on its own is usually A Bad Idea, especially if the others are worn a little. You don’t want to chuck some random tyre on one corner in isolation, all tyres are definitely not equal.

Different tread patterns or compounds side-to-side is a HUGE handling/safety no-no, and having one worn and one new tyre on the driven wheels especially (or anywhere if the car is AWD) can destroy diffs or AWD clutch packs.

Two-wheel-drive car, you should be able to get away with only replacing the front or rears as a pair and you should be golden.