I wonder if recruiters recruiting recruits for recruiting are substantially better at it than when the same recruiters recruit for clients
Here in the UK that's called 'rec to rec' and I promise you, they are generally shockingly bad. If you think tech recruiters are incompetent and greedy then you would be horrified at the standard of rec to rec.
In my experience Agency recruiting (on behalf of another recruiting agency) is indeed usually done because the original recruiting agency couldn't fulfill the entire contract. So they find whoever will give them the highest markup from the smaller agencies and contract it out to them.
Kind of like picking the lowest possible bidder for a construction contract, it doesnt usually go well.