I don't see an attempt there to control for distance. If I'm reading it right, you've explored the variation in home advantage over time, between ballparks, and between teams (which turns out to be significantly different from ballparks - a surprising finding). The very last paragraph says you've left examining the effect of distance to "a better study". What am I missing?

I've seen results before from American sports saying travelling East is worse for a team than travelling West, because of jetlag effects, and travelling to Colorado is bad, because of altitude effects. Those results would be tricky to tease out with your approach: if West Coast teams consistently perform 5% worse when playing on the East Coast, you can't tell that apart from East Coast teams playing 5% worse on the West coast by looking solely at win rates. The study I'm thinking of did something clever with looking at multi-game series to evaluate the jetlag effect.

The assumption was that teams from the Midwest would suffer least if it were purely distance (as they have the least shift/average travel) but that didn't bear out.

Have they? They have to travel half the distance, 100% of the time, compared to the coastal teams who travel the full distance across America half the time. That's in the "spherical cow" situation where all the East teams play in New York and all the West Coast teams play in LA...but if you add up the real miles travelled its probably within 20%.

Sure, but they never\* have to travel the full coast-to-coast, which is presumably where the worst of its effects, if any, would be realized.