I've not had a problem registering both this and my phone on any site.
Avoiding the risks of short, weak passwords? The risks of reusing passwords across sites? The inconvenience of remembering loads of passwords? The frustration of having to type passwords manually? The risk of getting phished or typing one site's password into a different site? Remembering and typing usernames? The password manager takes care of all that for you already.
And if your objective is to have a second factor just in case your password manager gets compromised? A physical button just in case someone takes over your mouse and keyboard? Or a credential stored in a secure element that's (somewhat) protected even if you use it on a compromised machine? Putting it in a password manager (or OS keyring) removes those advantages.
Technically the place where you store your passkeys can be hacked into, but there is no technology that protects against that. You could give a tech layman 5FA and he’ll give all 5 factors to the nice man on the phone call.
Neither can passwords if you’re using a password manager to handle them.
So again, if you’ve already got a password manager, and would put your passkeys in a password manager, what is the benefit of passkeys?
Password managers should be the default authentication method, and the current hack of having it type text into a password field is both unwieldy and completely avoidable.
That's the benefit you get from passkeys that no password manager will otherwise be able to give you.