"The math" only matters for random collisions, which are effectively impossible (less likely than the CPU malfunctioning). However that tells you nothing about maliciously constructed files. Even if a hash function has no known collisions today, doesn't mean that they won't be found someday.
But as I tried to describe (probably in way too much detail) the real problem with "hash everything, compare hashes afterwards" is that it implies that you'll be doing I/O to read all of the file's contents even when it isn't needed to prove uniqueness. For a lot of common use cases (big files, few dupes) this can mean doing 1000x more I/O than you need.
Once you design the solution around avoiding unneeded I/O, you find that hashing also stops being useful.
But as I tried to describe (probably in way too much detail) the real problem with "hash everything, compare hashes afterwards" is that it implies that you'll be doing I/O to read all of the file's contents even when it isn't needed to prove uniqueness. For a lot of common use cases (big files, few dupes) this can mean doing 1000x more I/O than you need.
Once you design the solution around avoiding unneeded I/O, you find that hashing also stops being useful.