I want to preface this saying this is not a problem that needs solved, I'm just wondering out loud here.
There have been a few times this year where there's been a change of possession, followed by a significant delay in trying to switch team balls because everybody on the sideline is too busy celebrating. This got me thinking, what if we just had "game balls" rather than each team providing their own? In case of an interception or fumble, we just keep playing with that ball. We'd still have several for trading in after a long incompletion or similar, but we start enforcing the rules that state only officials can order the ball changed. Each team would be responsible for providing a ball boy to go retrieve balls out of play on their sideline and handing one to the wing official as needed, but not responsible for providing the balls themselves.
Maybe the white hat would be given 6 or 8 balls by whatever association and they ensure they're inflated/maintained/etc.. I wouldn't want to force a financial cost that the officials have the buy the balls, of course. This would also ensure that one team doesn't underinflate the balls, or use a worn out ball, or put stickum on them, etc.. Yeah, we check them before the game, but every time I've checked 4 or 5 balls, there's always a bag of 15 more on the sideline and nobody ever ensures those don't get used (although if an obviously flat ball comes in to the game, the umpire will usually kick it back out right away).
Anyway, how terrible is this idea? Would it be complete and total chaos for no reason?