There is more published every second than you can read/watch in a week, and this asymmetry is accelerating.

Credibility is one heuristic that let’s us figure out what might be worth investing time into, since your answer cannot be “everything”.

Definitely. Using credibility, or any other metric, to determine what to review is fine. Using credibility as part of the review itself is not something I agree with.

With respect to publishing, there is a significant volume of work, and we should be able to keep up with it long as people review as much as they publish.

If that's what you think, then enjoy reading the many thousands of papers published by shitty paper mill operations.

You seem to be conflating the problem of weak or no pear review (i.e. the reason why paper-mill publications are shitty), with the problem of judging a paper by the author's name and not purely by its content (i.e. what the OP proposed).