This is akin to a batch of identifiers the size of all Apple products, while still allowing the device owner (or Apple) to disavow a particular device if it is lost or stolen.
The implementation also ensures that the same device creating multiple identities for the same website will have no signing characteristics linking one account to the other.
There are already designs if you are quite sure you must have attestation and yet you don't want device identification. You can do blinded attestation and agl has written up a much fancier approach on his blog too.
But again, Don't Ask, Don't Tell. The video shows this silly demo "Shiny picture" site asking for attestation and that's a bad idea you should not replicate, write "none" instead of "direct" and then the problem goes away for your site.
In WebAuthn the design is that a batch of (at least 1000 but usually far more) authenticator products should have such a document which Javascript can optionally request (together with proof they didn't just knock it off from another authenticator) when using the authenticator.
If you demand multi-factor and aren't willing to take my word (as the user) that I'm using it, you could insist upon seeing the attestation and reject authenticators unless you can see the attestation and you like it. For example maybe Great American Bank accepts Yubikeys, but rejects the Apple iPhone because they believe Steve Jobs was Satan.
Most sites should not use attestation at all. Firefox in particular can tell a site to fuck off when it asks for attestation. I'm happy to use high security WebAuthn but I don't want to have to tell you which products I use to do it. If your site does not require WebAuthn for every user then almost by definition it makes no sense to demand attestation from users who choose to enable it.
The use of "batches" is a privacy safeguard. If you permit attestation a site might know you have a Mattel Barbie Authenticator, but it won't know which one. If Mattel aren't selling many they probably put the same batch on the Buzz Lightyear Authenticator so a site can't even tell if you've got a Barbie or Buzz Lightyear.
According to this video apparently (?) Apple thought that wasn't safe enough and so it has decided to do something else weird instead, but not yet. Whatever, for almost all web sites you should refuse attestation if given the option. Maybe my bank needs to know I'm doing MFA with a high quality product but there's no reason Facebook or GMail or anybody like that should ask.