> The first seems like it would be very frustrating if code with failing tests if pushed with any frequency, but seems to be literally what the phase "work on main" means.

Yep, that's the point - it's to discourage devs from checking in failing code (because then they'll be swarmed by annoyed coworkers). It's fairly common to see developer A make a breaking change to some low-level library and then see developer B push a rollback of A's changes a few minutes later (with or without A's permission).