Googlebot has no problem identifying itself because Google knows that you want it to index your site if you want visitors. It doesn't identify itself to give you the option to block it. It identifies itself so you don't.

I care much less about being indexed by Google as much as you might think.

Google bot doesn't get blocked from my server primarily because it's a *very* well behaved bot. It sends a lot of requests, but it's very kind, and has never acted in a way that could overload my server. It respects robots.txt, and identifies itself multiple times.

Google bot doesn't get blocked, because it's a well behaved bot that eagerly follows the rules. I wouldn't underestimate how far that goes towards the reason it doesn't get blocked. Much more than the power gained by being google search.