It kinda kills the entire idea of time travel because of the "infinite" possible years ahead and the (as stated) lack of people visiting us now and thousand years back++. However that is also a counterargument, because of the "infinite" years ahead, the last thousand years or so might not be of any interest to travel to at all.
Its not infinite really as the Timetravel still has to exist within the rules of the universe which clearly show that there is no possible time travel to a point BEFORE the first time travel device was constructed, therefor the "Going back in time" idea is completely incorrect... furthermore the "Infinite" time into the future is also a flawed concept that ignores the fact that 29Billion years from now the universe will enter a "Radioactive death", in which all matter will begin to decay down into its most basic form. Based on the theory of multiple universes we can conclude that though we may live in a universe thats "Just right" the other universes will likely all either have had a constant "Death" state or will exist purely in a Plasma bubble that our own universe once existed in, and without Quantum Discord to disrupt the Plasma bubble state these other universes are as stated earlier, Sterile.
You could therefore travel forward intime to a certain point, but the concept of going back in time is only ever put forward for Hollywood or by people who fail to understand the Non-Liner flow of time.