I would say if you take a room full of programmers and select only the ones who managed to do the first 100 PE problems, you'll lose a lot of good ones that way. But all the ones you do select are almost sure to be pretty good, so in that regard it is an effective filter, plus then you get to complain about a lack of candidates and lobby for more tax breaks or whatever.
Maybe true, but you only have to worry about that if there are none left after your filtering operation. You are not trying to mine gold (find as many small nuggets as you can of a very rare substance among millions of tons of dirt). You are trying to find exactly N nuggets for some small N, that is the number of open slots you are trying to fill. If you can replace megabucks of excavation equipment (time-consuming interviews) with a simple screen (solve 100 PE problems) and N nuggets get through, you have saved yourself a lot of trouble.
Add to that, FAANG interview processes are mostly risk avoidant. They are more aimed at avoiding hiring bad candidates, than avoiding ignoring good ones. It is very often possible for a weak candidate to bullshit their way through interviews etc. Solving PE problems is harder to fake, at least without faking on purpose (by reading up on spoilers).
