How do you login to sites on your phone?
For less-sensitive sites (i.e. things that aren't going to screw me over if my account is hacked), I just save the computed password into the Chrome password manager. The computed password can't be feasibly used to get my master password anyway.
For many sites it's possible to stay logged in with a session cookie without saving the password.
What does this give you that, say, KeePass doesn't?