I'm amused that you got pushback. Just going on the metaphor, the very way that we check heartbeats in people is by a proof of work in some other part of the body. Isn't like we are directly hooked into the heart. It isn't like the heart sends out an otherwise useless signal.
We end up adding real work to the status checks often enough anyway, to make sure the database is still visible and other services. So inference has a lot of power that a heartbeat does not.