Why does it matter that the warlock short rests? Unless the party is actively moving, there's no obligation that the entire party must short rest at once. So the warlock can simply say "keep looking around, I'll take a short rest and regain my slots."
Because the rest of the party is, in general, incentivized to also short rest if one person is able to take one. You can spend HD, you regain any short-rest features you may have (more relevant for some classes than others, see below). Splitting the party is (almost) always a bad plan, and if one person is genuinely truly safe and comfortable enough to rest reliably, it's not clear why
everyone wouldn't be.
It's not really abusing the system either.
Try selling a typical 5e DM on this logic. I'd be impressed if you get even a 25% success rate. "It's not really
breaking the rules..." is exactly the kind of argument that fails the smell test for most DMs regardless of edition.
I don't know why a different player would feel compelled to rest when a different character can simply rest while they move. And a smart party could invest in a carriage so that even when the party moving, the warlock can still short rest.
Many DMs don't actually seem to buy that you
can rest while you move. The description given is, "A short rest is a period of downtime, at least 1 hour long, during which a character does nothing more strenuous than eating, drinking, reading, and tending to wounds." Walking or horseback riding doesn't fly for a pretty significant number of 5e DMs out there. Your carriage idea works....but is now actually making the warlock special, getting special attention and/or resources in order to pull the plan off. That's going to ruffle some feathers in at least
some groups.
Further: (BM) Fighters, Barbarians, Clerics, Druids, Bards, and probably more classes besides all actually
do want to take a short rest if they have the opportunity. Battle Masters get their dice back, Barbarians (at 11 for all Barbs, with Relentless Rage; earlier for Totem and Beast), Clerics get Channel Divinity back (doubly useful since Tasha's added Harness Divine Power to regain spell slots), Druids get wild shape back (and many subclasses thus get more uses of their key features), Bards get their Bardic Inspiration back at 5th level (and various subclasses get stuff back on SR at other levels). Even the party Wizard, the would-be king of long-rest-based characters, usually wants in on at least one SR a day because of Arcane Recovery. Add in spending Hit Dice and any other benefits, and it's unclear why you'd make space for
just one character to take short rests whenever they want.
Plus...there could easily be some resentment going on here. "Sorry guys, can't help you with whatever you're doing right now, I gotta take a short rest first."
Kinda thematic too, right. "Oh, we need someone to change all of our appearances. Let's ask the warlock meditating in the carriage whether he can do it." "Yes, my connection with the Archfey allows me to adjust our appearance. I shall cast the spell, then I shall take a moment to concentrate on my magical power again."
It seems like this is the intended way for Warlocks to be played outside of combat. It's like if a group was actively making sure the wizard doesn't have enough gold to copy spells into their book. That would suck for the wizard player because they're not allowed to play their game.
Yeah, sorry, I don't see it. If short rests were still 4e-style, that is, only five minutes, then yeah I'd totally buy that this was intended. With them being a full hour and (at least in principle) somewhat restrictive in what activities you can perform, it doesn't strike me as "intended" that Warlocks be taking tons and tons of rests while the rest of the party....waits, apparently? Or adventures without them? Or something?
But yes, you're correct that it IS just like making sure the Wizard doesn't have enough gold to copy spells.
That's the problem. The game, and the DMs, and even the players themselves, are incentivized to
not let the Warlock do this, even though it probably would be more effective--because it
feels unfair, because it
looks suspicious, because most people
don't feel it's thematic, and (as noted elsewhere) because you really
can't rely on there being only one fight per day and lots and lots of ample "really doing not much of anything" time. (Frankly, even presuming you can buy a carriage for the warlock to rest in is a bridge too far for many DMs!)