Credentials being "remotely stored" would be the case regardless of if you run any other viable storage such as Dropbox. I suppose you can remotely store on your own server, but I'm about a million times more likely to screw up than even a bad cloud company or password manager - so that's a non starter.
I'm sure there are alternatives to LastPass/1pass and similar, but storing encrypted passwords in a local file solves only a small part of the problem.