Interesting...
I just learned that the Baseball HOF does not -- and has not since 2001 -- allowed players and managers to select which cap appears on their plaques. Apparently, the change was made in part because of rumors that players were receiving compensation (e.g., money or a retired number) in exchange for selecting a particular team to appear on their HOF plaque cap. In particular, there was a story (which he vehemently denied) that Wade Boggs's contract with the Devil Rays required him to select a Rays cap to appear on his HOF plaque. This came into play with guys like Gary Carter and Andre Dawson. They wanted their plaques to depict, respectively, Mets and Cubs caps, but the HOF decided both would have Expos caps. It does appear, though, that the HOF will give greater deference to a player who wants to be depicted with no logo on his plaque cap (e.g., Tony LaRussa and Greg Maddox).
Notwithstanding my dissatisfaction with the selection process, visiting the HOF was awesome, and I need to do it again. I went there in January 1996, during the week leading up to my wedding in Albany. I went with one of my groomsmen who wasn't as into it as I was, so we only spent a couple hours there.