The dog that didn't bark... at E.T. in the shed

Is it just me, or are the odds that we'll find demonstrable proof that aliens visited Earth really, really low?

Consider the following:

1) If aliens had visited Earth anytime in the last two or three thousand years, there would not only be conclusive proof, but the aliens wouldn't have kept it a secret. I don't see why they'd come all this way and then just hide. Why?

2) Having the technology to travel from some distant solar system to Earth correlates with having the technology to defend yourself rather well. Visiting Earth, aliens probably wouldn't be very frightened.

3) Or suppose they were helpless and desperate. What good would hiding do? "Damn, we really need their help, or resources, or something. But let's not make our presence known, it would be rude."

4) But those three reasons are bullshit compared this simple one: That if alien had ever visited Earth during recordable history, it would be a huge coincidence. Look, the natural history of Earth is a split-second relative to the history of the universe, which would make recorded history a split-split second. It's not as if other species evolving on other planets, apt for the sort of ratiocination necessary to develop the technology to travel interstellarly, would necessarily be evolving concurrently with the evolution of humans on Earth. Such evolution could have begun millions of years prior to the natural history of Earth (or may begin millions of years after humans are extinct). And so if the chances of such a species were high, you'd think they would have already contacted us. Or, considering how recorded history on Earth is a fraction of a second relative to the natural history of Earth, you'd think, if aliens ever visited Earth and decided not to stay or leave a calling card, they would have visited Earth during a period of time before recorded history.

I'm not saying there are no aliens- The probability that there aren't or weren't or will never be aliens is very low, considering nothing else than the vast number of solar systems and stars and galaxies and vast opportunities for such a species to evolve. But that such a species were to evolve concurrently with humans, having the technology for interstellar travel and us not having been made aware of it yet... Pretty unlikely.