Forget the usually discussed paradox about time travel; how about how one would know whether one had come back to the proper (intended) present?
Would one rely on clocks and calendars? Clocks move at different speeds (as explained by relativity). And how much should the calendar have changed while you were off in the past? Does the travel itself take any time? How about if everyone else also time-traveled while you were off doing that? Who, or what, decides what the correct time is “back home”? (To say that it would take so much energy that only one person should be able to time-travel or get close to the speed of light at a time would be an economic argument, not a physical one, so in a discussion of physics, we must allow for the possibility that everyone is time-traveling concurrently—let’s say, by starting together but going off in different directions in different amounts.) Then who or what keeps so-called real time going in its regular pace? (It doesn’t even have one, thanks to relativity!)
What we mean by time travel—if it’s not kept track of via clocks—is that causality is unaware of the traveler’s appearance and disappearance. So, what happens to the air molecules where the traveler will suddenly appear? Are they pushed out, or do they somehow combine or coexist with the traveler’s? If they are pushed out, then how massive an object can time-travel? (Because, at some point, we’d be moving so much air, it would lead to catastrophic damage to someone or something. So, the paradoxes extends to the legal and safety realms as well, although those are merely practical.)