Really interesting (any tricky) question! These paradoxes definitely present a problem. Then again, who knows what would *really* happen? As humans I don’t think we can fully grasp the implications of such a fundamental ‘disturbance’ to what we think reality is.
I expect time travel would do more harm than good though!
If time travel were possible, wouldn’t our future selves (or an intelligent alien civilization) have developed it and wouldn’t they have travelled back to our time already? I don’t think we would see any paradoxes, unless we did the time traveling ourselves. To us non-time travelers, I think it would just be reality as usual. I would guess that is time travel is ever invented, the government would impose all sorts of rules and regulations on it. I think that if we do manage to travel back in time, it might be that there is a physical limitation that we can only observe and not influence the other time. That would prevent any possible paradoxes.