You assume most people have the patience to copy paste passwords from Bitwarden rather than the ease of Lastpass - just doesn't work for 99% of the population.
I don't know about Keywarden, but KeePass just uses a global hotkey that can be used to type in your password in a context-dependent fashion (figures out the relevant password from the page you're on). No browser integration required, yet no UX hit. (Edit: But I have no idea if its "figure out what page you're on" functionality would work with Bonsai.)
A password manager integrated with a browser can offer more security, because it can verify the domain to prevent copy-pasting the password into a phishing site.
Having your password manager tied to your browser is more secure because the saved password doesn't show up unless you're in the correct domain, preventing phishing attacks.