This annoys me too, but since starting work at a company which uses single sign on, it's started to make sense why certain sites have this pattern, e.g. if your login is an email address and the domain is enrolled to handle sign on outside of the service, you are redirected and the original website doesn't have the ability to capture your password.

For personal use, I find 1Password typically handles multiple screen logins, including 2FA quite well, although requires an extra UI interaction.