Is there not a time travel conundrum?

Time travel in movies, TV, and stories are supposed to be interesting. They believe they have a logical way to explain how the time travel occurs, and how they can track the date they want to dial in. There is a conundrum though. Even if you could muster up enough power to send anything back in time, that would throw the balance of everything off. As with many popular time travel stories, a person, group of people or an object is sent back, as an individual entity. There are two opposing scenarios, neither of them jive.

The universe is like the human body, there is very little you can remove without effecting the rest. If you were, say, to send the Earth and moon back in time. That would leave the present day solar system unbalanced because it would have no Earth and moon. So you would have to take at least the whole solar system back too. It would not be as if you sent one asteroid back, because it would not be missed in the greater balance of the universe, or solar system.

If you sent the present day solar system back in time, where would it be? The past would already have a solar system so you cannot imprint the present over the past, because only one solar system can exist at the same time, unless you are going to have an alternate Earth and solar system in the same time stream, but that is not truly going back in time on the Earth though.

There is a conundrum there. How would you suppose there would be a solution to that? Or the conundrum of creating enough power to move something as large as the Earth or solar system through time much less across the galaxy?