Arbitrary filtering of candidates is always an option, but then you may as well do it as cheaply as possible. Throw out half the resumes.

Arbitrary filtering of candidates doesn't reduce the effort that it takes. Let's say 1 out of 1000 of the candidates you see is what you need. The total amount of effort to find the right candidate is still the same. But throwing out half the resumes just doubles the amount of time until you find the candidate you need (you just spread lower effort over a longer time).

On the other hand if you "raise your bar" (let's say you do so by some method that makes it twice as expensive to judge a candidate; twice as likely to reject a candidate that would fit what you need, i.e. doubles your false negative rate; but cuts down on the number of applications by 10x, so that now 1 out of 100 candidates are what you need, which isn't that far off the mark for certain kinds of things), you cut down the effort (and time) you need to spend on finding a candidate by over double.

EDIT: On reflection I think we're mainly talking past each other. You are thinking of a scenario where all stages take roughly the same amount of effort/time, whereas tmorel and I are thinking of a scenario where different stages take different amounts of effort/time. If you "raise the bar" on the stages that take less amount of effort/time (assuming that those stages still have some amount of selection usefulness) then you will reduce the overall amount of time/energy spent on hiring someone that meets your final bar.