If time travel is possible, then the present is the past for an infinite number of futures. (Assuming the time stream is changeable by travelers, and not fixed).
In an infinite number of futures, there are a sub-infinity number of those futures in which a time traveler exists who finds today, the day you are reading this blog post, a fascinating and pivotal moment in history.
Therefore, even if only a small fraction of those infinite future travelers obsessed with our today actually bother/have the means to travel to today, there are still an infinite number of them.
Therefore, today there should have been an infinite number of time travelers appearing from an infinite number of different futures. Or, as Douglas Adams would have said, “whop”
Of course the same argument holds for every moment of every day in all of recorded history, so basically we should be inundated with infinite numbers of time travelers arriving at every moment of time for all time.
Since that is clearly not happening, time travel must be impossible.
I’d love to see a What-If XKCD on the idea of an infinite number of time travelers arriving today, actually… would probably be a mass extinction, the Earth would suffer gravitational collapse, and we’d be in a black hole. I think.