There are several time arrows, expansion of the universe, entropy increase, and your perception of future and the past. The last two are not independent at all, as your perception of the past is based on the memory which in turn is a chemical process that follows entropy increase. So the answer to "why things do not happen backwards in time more often" is that because your perception of direction of time is always aligned with the entropy increase.
Yeah, didn't Hawking write about cosmological versus thermodynamic versus perceptual arrows of time, in A Brief History of Time, like 20+ years ago? (Therefore I assume it was well-established even before that).
Plus, I may be missing something, but what's the difference between the self-indexical principle and the anthropic principle?
There are several time arrows, expansion of the universe, entropy increase, and your perception of future and the past. The last two are not independent at all, as your perception of the past is based on the memory which in turn is a chemical process that follows entropy increase. So the answer to "why things do not happen backwards in time more often" is that because your perception of direction of time is always aligned with the entropy increase.