Aside from the fact that the state of the art in science suggests that one (prediction) is possible and the other (time travel) is impossible?

But I think the more important issue is that assigning time-travel powers to Omega makes the problem much less interesting. It is essentially fighting the hypothetical, because the thought experiment is intended to shed some light on the concept of "pre-commitment." Pre-commitment is not particularly interesting if Omega can time-travel. In short, changing the topic of conversation, but not admitting you are changing the topic, is perceived as rude.