Indeed – I have a hard time believing that the vast majority of people who want one of these things wouldn't also want the other.

Hypothetical examples:

I don't want the New York Times to ID me, but I don't care if my wife knows I read it.

I don't want red tube to forget about my all access pass, but I don't want it in my browser history.

right, and i do want the times in my history so i know if i have seen it already. but as is suggested elsewhere, private mode does not prevent ID.

the times could switch to genuine browser/device fingerprinting and store that information server side. if they are careful enough so that false possibles are not possible (rather let a few slip through) then they could effectively control how much free access everyone gets.