He also breathes and gets fatigued though he has no muscles to fatigue. But since mortality is necessary to make it look like a being is defeatable:
* I don't think Brooke can regen using milk. Ussopp told him to stop joking, so I always took it as a joke.
* Bones heal much slower than muscles, skin, etc
* If Brooke's hair doesn't regrow, why would his bones? In this sense, Brooke's body is extremely fragile
In my opinion, breaking his body would break his spirit and kill him once more. I doubt that his fruit would work a second time, in fact I think it was implied it would not. Why else would he be more cowardly as a skeleton than he appeared in life?