That is a lot of hats but not as many as I would have thought. Granted there could be hundreds of other hats lurking under other categories. Not ribbing you, I have a lot of hats myself although I suspect you have more.
You'd be right and you'd wrong in assuming that.
About five years ago I went to buy a new Dodgers hat and discovered that my head was no longer a 7 1/2 but instead a 7 5/8. This was right after MLB switched from the old gray underbrim to black and implemented the new wicking material in their hats, which, I had long assumed, meant the end of being able to stretch out or shrink authentic on-field hats. As a result of this discovery, I wound up rebuying most of my old hats in the new style and trashed all of my old ones that I wasn't able to donate or give to my dad (a fellow hat addict).
I'd have a lot more hats but there are some teams I can never rep (Yankees, Red Sox, Phillies, Braves, Angels, Padres) and some teams that I would rep that have ugly hats on-field authentics (White Sox, Astros). One thing that I hope MLB continues doing is the "Turn Back the Clock" games. I bought a ton of hats that I always wanted to have an authentic on-field version of this past year that were only available with the New Era flag on the left side prior. The coolest of these hats being the block W Nationals hat, the all black Padres, the Brooklyn Dodgers B, and the Seattle Mariners '80s pitchfork. I would have gotten the Kansas City Royals red "TBTC" hat but it had a red underbrim, which looked clownish.
My favorite hat, which I hope this team never moves away from is this:
With this one a close, close second: