They should be portable. I don't know if they should be stored in the cloud though. Ideally you can open a password database in whatever application you want if you have the database and login information. Not allowing this is inconvenient and doesn't seriously increase security.

Having them not be portable ensures people use them less frequently. If I couldn't sync mine between my phone and desktop I probably wouldn't use it. The way I do it isn't built into my manager (KeepassDX), but I use Syncthing to keep it up to date on both devices. It'd be better if there was an official option for people bad with technology.