to prove evidence (such as a video) has not been tampered with by hashing files into a blockchain during the formal intake procedure. etc. OK, but is this a problem? Does evidence routinely get tampered with?

Probably not on a wide scale, but even the suspicion that it is may be sufficient to undermine the authority of, say, an archive of record. Being able to demonstrate that the document you're looking at is the same as the document received by the archive (or at least recorded in its catalogue) however many years ago is probably a good thing. Often archives don't present the actual file they received, they present a version of it - downscaled, converted to PDF, partially redacted, or whatever. In that case, being able to demonstrate the provenance - we started with this file, transformed it in such-and-such-a-way on this date, etc - would still be very valuable. My feeling is there may be a useful application in this area, but then I probably would - http://www.archangel.ac.uk/publications/ - but I'm not aware that it's actively being pursued at the moment. All the other purported applications? Bunch of arse!