Yes. A lot of the common solutions to making TOTP more user-friendly defeat it. You might as well just use single-factor auth with a strong random password stored in your manager, which is what I do.
The threat model is someone gets your password, not somebody gets access to your password manager.
If the latter is your threat model then yes having your 2F in there is worse, but really the former is the more common thing to protect against and the tradeoff of not having 2F in your 1Password and getting locked out because your phone breaks is worse than the risk of having it in there.
It’s similar to the tradeoff of having a nano yubikey always in your laptop or a large one on your keys. For most people the nano is better (though you should have a second one in either case)
If you're using a password manager, you probably have one-time secure passwords, so the only probable way someone gets it is by stealing your password manager.
So the attacker gets access to the plaintext passwords but not the rest of the database or the ability to skip the 2FA server-side, and the site doesn't notice. Guess I can see that happening still, since the password DB is likely separate.
They aren't accessed often, are not used during your normal login flow, and provide you a recovery mechanism that actually works.
Yes - you should store them as securely as you can, but I'd say this is better than disabling 2fa entirely, which seems like the other sane approach.