If a baseball player has an equipment issue, like a broken glove or bat, an umpire grants time out and the player gets to fix things.
Try that in football or basketball.
In football, if a shoulder pad trap breaks, the player either quickly gets replaced before the next play begins or takes his chances.
In basketball if a shoelace comes undone or the shoe comes off, tough luck. Play on. A million years ago I attended an NBA doubleheader at Madison Square Garden. In the first game the Boston Celtics played a bad team. In the second game the Knicks played another bad team. In the first game Celtic player-coach Bill Russell threw a shoe. Back then Boston wore black low cut sneakers. Instead of calling time out, Russell picked up his shoe and played on until there was a natural stoppage a couple of plays later.
Baseball should have that same natural flow, including accepting natural penalties when stuff happens. In baseball if the wind blows dust at the batter the umpire calls time to save the batter. In football if that happens, the play continues. It could continue in baseball, too. The batter could protect himself by stepping out and accepting the natural penalty that should attach: the pitcher throws one right down Broadway for an easy strike.
If an outfielder needs his sunglasses retrieved, play should continue, even if the fielding team plays short handed. In fact, that is a good idea for other reasons.
How about giving the batting team the option of taking a walk or having the fielding team play short for the next batter? A power play. It could also be a punishment for bad behavior, such as hitting a batter with a pitch. Let them play for a while with fewer fielders. Hey, then there would be some interesting strategy.
I've played slow pitch softball games in which a team played without all its fielders, even once with only 8, the minimum allowed. They tended to leave second base empty. I thought it made more sense to leave third empty and let the pitcher cover. In slow pitch, pulling a grounder to third is more difficult than grounding one through the right side. Plus, it kept things normal for covering second.
Anyway, you get the idea. Introduce some different twists, both to speed things up and to add some real decision making, which could best be done by allowing re-entry.