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> Researchers have to wait forever and a day to get their papers approved, [...]

In Physics the standard time is like 3 month. I guess Chemistry and other applied areas had similar times. Anyway, the review time for Math is insane and I've heard a few horror stories of more than one year from close friends.

> [...] and field experts didn't pick the one profession that’s most unlike a Got Talent panel judge to end up giving a critique on some postgraduate student's homework.

This is a very inaccurate characterization. Nobody is peer reviewing postgraduate student's homework. The paper is written by the research group. The postgraduate student probably did a big chunk of the work but unless the advisor/group chief is a moron the paper is improved and fixed before it's submitted to be review in the journal.