That’s part of it, but compilers also use the information more directly especially in languages with inexpressive type systems e.g. dereferencing a null pointer

That’s part of it, but compilers also use the information more directly especially in languages with inexpressive type systems e.g. dereferencing a null pointer is UB so the compiler will tag a dereferenced pointer as “non-null”, then will propagate this constraint and remove unnecessary checks (e.g. any check downstream from the dereference, or unconditionally leading to it).