Storing 2FA codes is just the beginning. Bitwarden aims to add defense in depth to authentication.
Bitwarden Authenticator is a standalone app that is available for everyone, even non-Bitwarden customers.
In its current release, Bitwarden Authenticator generates time-based one-time passwords (TOTP) for users who want to add an extra layer of 2FA security to their logins.
There is a comprehensive roadmap planned with additional functionality.
Exactly, from a security perspective, it's a bad idea to put 2 factor tokens together with your passwords. You effectively eliminate the security benefit that 2 factor provides if you do because if people get into your password manager, they have everything they need to access your accounts. The only people it "helps" having it all in one app are people who don't understand the purpose of 2 factor and just see it as an inconvenience when services force it on them. Even though I use BitWarden for passwords, I don't think that I'll be changing from Aegis to BitWarden's stand-alone authenticator because Aegis is doing its job nicely.
It really depends on your threat model. It’s not a one size fits all thing.
For instance in some threat models you shouldn't have TOTP auth and passwords on the same device, let alone the same app, but the vast majority of people are not going to carry two devices because of how inconvenient it is.