Others have mentioned that compilers take advantage of these things for optimization, but haven't mentioned that compilers will still often do unexpected things

Others have mentioned that compilers take advantage of these things for optimization, but haven't mentioned that compilers will still often do unexpected things when encountering UB with optimizations off. Turning optimizations on doesn't suddenly undefine any behavior, it just changes what the compiler does when encountering some of those behaviors (among other, non-UB based optimizations). A non-optimizing compiler and an optimizing compiler both have to conform to the standard.