Nope. If a pitch clock can be implemented a transition clock can too. One minute is enough. Between the plethora of coaches in the dugout and players not in the lineup each player who is on the bases, batting, or on deck can have a designated equipment handler to facilitate a quick exchange. Hustle in, hustle out, and resume the game. Bathroom and water breaks can be done at other times.
This is feasible and it's the simplest, most logical, and most efficient approach to minimizing in-game down time because the duration of the between-half-innings break is the single biggest contributor to the problem. My understanding is the minimum length of a break is 2:15 so in reality I suspect it's about 3 minutes from third out to first pitch almost every time. With 16 or 17 such breaks in a 9-inning game, going to a 60-second break would decrease the running time of a typical game by 32-34 minutes.
Of course, the obvious flaw here is that minimizing in-game down time is not the goal these rule changes are seeking to address. MLB's one and only objective in everything they do is to maximize owner profit. Any and all changes made are done to further that goal and that goal alone.