That does sound bizarre to me. When we've got fighters, monks, and warlocks in the party, we usually don't have much of a problem with players agreeing to take a short rest when asked. I don't know if my players are just more effective at advocating for themselves or just recognize that those classes are better off if they've taken a short rest, but getting multiple short rests per long rest isn't usually a problem for us.
There are so many other examples over the years of players in the TTRPG community really not grokking the dynamics of cooperative, non-competitive games that I sometimes get really depressed about the community.
It's not really about being non-cooperative. It's about evaluating and balancing the risk of taking a rest -- which technically isn't always there, but essentially it always is a consideration in the players' minds -- against the risk of that one PC not having abilities in future encounters.
The player playing a short-rest-limited class
chose that class, knowing how it operates. They also
chose to spend their abilities the way they did. It's not right that the rest of the table should bear the cost of the short-rest PC's shortsightedness. Nor should they encourage that shortsighted behavior by always bearing that burden after every encounter, which is precisely what you'd be encouraging. We're back at the problem that the game mechanically rewards players for constantly resting, and the primary reason not to do so is narrative (NPCs responding to the PCs, or time pressure).
I mean, the same thing happens if the sorcerer spends all his spell slots and sorcery points in one encounter while nobody else did. You're going to be stuck flinging cantrips for a bit. Or if the paladin busts out two weapons and goes supernova. You get to play fighter for the afternoon. Part of the game is proper resource management.
On the flip side, when the long-rest-limited classes run out of abilities, it tends to happen about the same time across the board, at the same rate as other long-rest PCs, or at about when HP get low. That's kind of how you know you've managed resources well. The fact that short-rest limited classes could keep going doesn't help because you're unlikely to split the party like that.
It's exacerbated because short rest hp recovery has attrition that spans long rests. It's nearly the only mechanic in the game that has multiple-day recovery. Spending HD to recover hp today means fewer HD tomorrow. Counterintuitively, short rests are
more expensive than long rests for hp recovery! It's so bizarre to me that they made that choice to add attrition back into the game only
there.