okay so in principle everything is technically discretized if not outright quantized because the set of values a computer can store is finite, but the use of like, floating point values in video games that are not provided by the system, regardless of precision, i feel like should generally be treated very carefully
this isn't to say you need to like, eliminate all subpixels, just that if your player needs to, for example, rotate objects to solve puzzles, it's worth considering if the system is better served by having a set of fixed angles the object can be in, rather than allowing it to be at arbitrary angles and then deal with tolerances on an irregular range
this isn't suitable for every game or application, but for me, i find it valuable to think about as a first option in a lot of cases. also i think it would be interesting to play a 3D game where the player can move forward or backward continuously, but can only rotate in 45° increments