Do it right and the blockchain can provide trust by ensuring that the record demonstrates that a sufficient number of other parties have confirmed each part of the record.

You have a point in that if an archive is trusted the motivations for doing this largely falls away. The problem is of course that we don't know if the archive will always be trustworthy (e.g. at some point they may accidentally hire someone who is not trustworthy into a position where they are able to do damage), and if/when they're not is when they're likely to be most resistant to putting in place means to prove they are trustworthy.