So Locality-sensitive hashing has basically the opposite goal of a cryptographic hash function, where a single bit change in the input should result in a significant change in the output?

What if there's a legitimate, private file uploaded to Megaupload's hypothetical successor, but someone uploads a highly-similar file publicly that gets a takedown notice?

The problem with forcing digital locker sites to remove content by hash rather than by URL is that it's impossible for them to know whether some of the URLs that point to a given hash are legitimate (e.g. a FLAC file being transferred by a musician to their CD pressing company and a select set of friends, but someone leaks the FLAC files and they get re-uploaded and deduped). This problem would be exacerbated by using a fuzzy or locality-sensitive hash rather than a cryptographic hash.