This is partially because browsers don't have decent API to handle basic auth. Bitwarden will log you in via basic auth if you only have 1 matching entry for the URL but surely things can be better than this...
Are you suggesting password manager devs start sending patches to browsers? Getting used to all browser API isn't exactly easy to begin with, let alone there aren't many who has enough motivation to wait for that implementation to become wide spread for it to finally solve a problem that is only used by a few.