> Empirically the coin should should converge to 50% of the flips reading Heads, so why does betting on a Heads not make sense when you've been seeing too many Tails?

If you knew, a priori, that 75% of the next 4 flips will land on H, and you've seen THH, you are justified in guessing H. In this scenario, H was actually due.

I think it's clear that real coins make no such promises.