> It does not eliminate code reviews.
Yes it does. There are many ways to do things, of course, and you can institute that there must be an independent reviewer, but I see this is a colossal waste of time and takes away one of the many benefits of pairing. Switch pairs frequently, and by frequently I really mean "daily," and there is no need for review. This also covers "no fixed responsibilities" you mentioned (which I absolutely agree with).
Again, there are no rules for how things must be done, but this is my experience of three straight years working this way and it was highly effective.
Mixed-level pairs (senior/junior), for example, are more about mentoring than reviewing. Those sessions do not qualify for "more than one pair of eyes".
Excited (or maybe even stubborn) developers can often win their pairs by exhaustion, leading to "whatever you want" low effort contributions.
Pairs tend to under-document. They share an understanding they developed during the pairing session and forget to add important information or details to the PR or documentation channels.
I'm glad it has been working for you. Maybe you work in a stellar team that doesn't have those issues. However, there are many scenarios that benefit a lot from an independent reviewer.