- No magic artificial gravity; and
- NO TIME TRAVEL.
The reason I don't like the idea is a very straightforward one - when first examined, it completely negates the concept of free will. Though this question does crop up for the time travellers involved directly in "making history," I'm thinking more in the grand scheme. While the time travellers may question whether or not they're just the instruments of history, a predestination paradox effectively reduces everyone else to deterministic automatons.
This aspect may not be immediately obvious - it took me years to realize the implications, but the implications do nonetheless exist. The people other than the time travellers, from the moment they arrive in the past to the instant they depart the future, must not have any free will - because, otherwise, the time travellers might never have the opportunity to travel through time in the first place. Choices deep in history resonate chaotically, and an innocuous decision made in the past could prevent the time travellers from ever being born. Entire lifetimes could easily be spent within the "locked-down zone" between future and past, billions of people following a script they can never see, to ensure that history unfolds as it needs to, and no one would really be responsible for their actions - after all, they didn't have a choice.
I find it rather disturbing, personally. I don't plan right now to do any time travel-related work, but if I did, I would do what I could to get around the question of predestination. The idea of the observer effect has a particular appeal to me - rather than get all caught up in the issues of the absence of free will, I'd rather explore the implications of time, from a non-linear and non-subjective viewpoint, actually unfolding in anachronic order. Time travellers from 2050 going back to 1750 wouldn't, in this case, worry about creating three hundred years of determination, because technically speaking 1750 hadn't happened yet.
It's just an idea that comes with plenty of headaches - so well fitted, I think, for something to do with time travel.