There. That's it. All this is a far-from-optimal filter for the total strangers. Get a foot in the door with an established insider and you get right to the last interview(s). No WBs, no take-home projects.

Does this actually work in practice? From my understanding knowing someone might get you past the initial HR / ATS hell to a first round, but you mostly have to follow typical processes after that.

In some cases yes.

In my experience they were even apologetic "sorry, we have to do this, let's get over it".

Once the pull to get you in is in place - it will help to put a checkmark in internal bureaucracy checklist and minimize unrelated interactions.