(It still protects against a password leak, though, so doesn't entirely defeat the purpose of MFA.)
By and large, I see it as protection for the service provider, not for the me - they prevent the service provider from having to deal with people using weak passwords or re-using passwords that get leaked.
By-and-large, given the option, I wouldn't enable MFA - I appropriately store my strong, unique passwords, and am satisfied with that level of security.
Having MFA forced on my is purely a convenience downgrade without any real security upgrade, and having my password manager automatically fill MFA tokens minimizes that convenience downgrade.
Keeping the password and MFA secret in the same password manager reduces separation (if someone fully compromises your vault, they will gain access to both factors). But that doesn’t make MFA pointless; it just means it doesn’t protect you against that particular failure mode.
And if someone has full access to your password manager, you already have a much bigger problem.