I think "provide their own footballs" can be a little misleading. It isn't like they can go out and purchase whatever brand and model they want. Teams have custody of the league approved balls and can prepare them how they see fit within the league specification. So while there is room for a little customization, it fits well within jonshariat's overall point of standardized equipment.

But shoes? Gloves? Glare reducing eye makeup? Socks? Hydration drinks?

The list can basically go on forever. With no real "a priori" idea on where you have to stop to no longer find a benefit in equipment. Could even go back to "access to gym" or "access to trainer" and expect a level of influence.