I consider the existence of door #2 a red flag. If decision makers who are likely not technical themselves are making that kind of decision about technical hires, odds are that they are going to make some very bad hires that I won't like living with.
That's not to say that there aren't a lot of companies where your advice works. But I'd prefer to work for the companies where it doesn't.
Even assuming that you're not a bad hire, it can still be a bad idea to allow this. If the decision makers can go over the heads of the people who are in charge of technical hiring and force them to take on someone they haven't vetted then that's just going to cause resentment.
I don't mind skipping HR so much. But skipping the technical-vetting step is bad. If your hiring-committee doesn't make good decisions, that's a separate problem that you should solve without just starting to ignore them.
I would suspect that "door #2" is most useful in the (more common at large companies than small?) case where a technical lead of some sort has a position on their team they want to fill, and HR is a barrier between them and the engineer(s) they want to bring on board.
That's not to say that there aren't a lot of companies where your advice works. But I'd prefer to work for the companies where it doesn't.