As someone who actually does both, this is IMHO backwards. My "password vault" is a GPG file I open in emacs and cut and paste from. It's trivially copied and maintained, extends cleanly to "non-password" secret info (e.g. credit cards, my kids' SSNs), involves no third party systems beyond the operation of the software, is trivially backed up via straightforward file copies that I do all the time anyway, and just in general works better than the rather complicated ecosystem of commercial offerings.
Works poorly in a phone, though.