In the context of almost every proposed causality violation mechanism I've seen seriously discussed, it really is can't, not won't. Wormholes aren't the only example. Tipler Cylinders for example don't allow time travel prior to the point when they started rotating. Godel's rotating universe has similar restrictions. Is there some time travel proposal I'm missing?

I agree that when considering anthropic issues won't becomes potentially relevant if we had any idea that time travel could potentially allow travel prior to the existence of the device in question. In that case, I'd actually argue in the other direction: if such machines could exist, I'd expect to see massive signs of such interference in the past.