But then what? Can the doctor protect his/herself?  If they can, they certainly can't protect the villagers at the same time.  And either they're left open to be killed, or they are effectively useless while the killer continues with their business.  The Doctor revealing themselves makes them considerably less useful.

And I doubt the killer sided against tabby.  The killer win condition is that killers outnumber villagers, and now they have to be the last one standing, which is considerably more difficult than the prior situation.  And yes, I am aware that this partially implicates me, but if the villagers win, even if I die, then I would view it as a victory for myself.