There are good reasons why frequent rests and the five-minute-day have become a thing. It's in the players' interest to seek to have full resources for each encounter, both out-of-game as players seeking to maximize their fun and in-game as faithfully roleplaying the desires and preferences of their characters.
I think a contributing factor is the lack of a middle ground when it comes to PC resources.
4e has powers that can be used at-will, per encounter (or technically recharged on a 5-minute short rest), or per day (recharging on an 8-hour long rest). This means you have some bread-and-butter stuff (which still usually has some effect beyond "I hit it", like pushing the enemy a square or giving an ally a bonus or something – nothing spectacular, but a little juice at least), a few fairly heavy-hitting attacks you can use 1/encounter, and then some big guns you can use 1/day. Since both encounter powers and, mostly, hit points recharge on a short 5-minute break, you go into every encounter at a fairly large proportion of your potential power. The main attrition isn't to your offense, but to your healing surges.
5e has, to a large degree, done away with encounter powers. For one thing, almost nothing recharges per encounter anymore. There are a handful of abilities that at high levels say something like "If you roll initiative with 0 foo remaining, you gain 1 foo" but that's pretty rare. There are some abilities that recharge on short rests, but a 5e short rest is a very different thing than a 4e short rest – 1 hour instead of 5 minutes. It's hard to imagine a situation where the PCs can take a short rest but not a long rest, barring external time pressure.
Short rest abilities are also usually a fairly small part of a class's abilities. Looking at 5.0, we have:
- Barbarian: A short rest resets the DC increase for Relentless Rage, a level 11 feature.
- Bard: Starting at level 5, their inspiration recharges on a short rest.
- Glamour bards recharge Enthralling Performance (level 3) and Unbreakable Majesty (level 14) on a short rest.
- Whisper bards recharge Words of Terror (level 3) and Mantle of Whispers (level 6) on a short rest.
- Clerics: recharge Channel Divinity on a short rest.
- Knowledge clerics also get an ability at 17th level that let them get some vague visions that recharge on a short rest.
- Druids: recharge Wild Shape on short rests. Particularly for Moon druids, this is a legit power ability.
- Land druids recover some spell slots on one short rest per day.
- Shepherd druids recharge their Spirit totem on a short rest.
- Fighters recharge Second Wind and Action Surge on a short rest. This is basically their limited resources so that's good.
- Many sub-classes also have resources that recharge on short rests. Notably the Battlemaster's superiority dice, the Arcane Archer's Arcane Shot, and the Gunslinger's Grit.
- Monks recharge Ki on a short rest, which is pretty neat.
- Paladins recharge Channel Divinity on a short rest.
- Rangers don't have any main class features that recharge on a short rest.
- Horizon Walkers recharge Detect Portal (level 3) and Ethereal Step (level 7).
- Monster Slayers recharge Magic-User's Nemesis (level 11).
- Rogues recharge their level 20 Stroke of Luck on a short rest.
- Soul Knives, much like Psi Warriors, recharge the ability to regain one Psionic Energy die on a short rest.
- Swashbucklers recharge their level 17 Master Duelist ability.
- Sorcerers at level 20 restore 4 sorcery points on a short rest.
- Divine Soul sorcerers recharge Favored by the Gods.
- Storm sorcerers recharge the level 17 ability to give their whole team flight for an hour.
- Warlocks recharge their Pact Magic on a short rest. This is a biggie.
- They also have a whole host of invocations and subclass abilities that recharge on a short rest, too many to list here (and many require you to actively select them instead of other abilities).
- Wizards regain some spell slots on one short rest per day. At level 20, they also recharge their two special Signature Spell slots on a short rest.
- A small number of subclasses also have abilities that recharge on a short rest, usually fairly high level abilities.
So, which classes benefit the most from a short rest? I'd rank them as such:
- Fighters, Monks, and Warlocks. These classes all have major resources tied to short rest recharges.
- Bards, Clerics, and Moon druids. Inspiration is an important feature for all bards, and Moon druids in particular use their wild shape a lot. For clerics it varies a little between domains as to how useful their Channel Divinity is – Life Domain's healing is awesome, but War's ability to turn a miss into a hit is less awesome.
- Other Druids, Paladins, and Wizards. For druids in general, wild shape is more of a utility power than a combat thing. Paladins have less Channel Divinity than Clerics, and it's usually not as strong. And wizards regain a spell slot, which is neat.
- Barbarian, Ranger, Rogue, and Sorcerer. These either regain nothing on a short rest, or the thing they regain is inconsequential, or only happens at high enough level to not matter in 95% of all campaigns.
I'd also note that there's a
big jump between rank 1 and 2. Fighters, monks, and warlocks have their main source of awesome tied to short rests. Bards, clerics, and Moon druids each have a very useful resource tied to them, but they are still primarily casters who recover their spell slots on a daily basis. For them, a short rest is nice to have but generally not super important, which it is for fighters, monks, and warlocks.
This, of course, can create tension in a party, where a cleric maybe has spent a third of their spells and one of their two Channel Divinities, the sorcerer is also down about 1/3 of their spells, while the fighter has spent both their Second Wind, their Action Surge, and all their Superiority dice, and the rogue has spent nothing because they have nothing to spend. The fighter would very much like to take a short rest now please, but the rogue and sorcerer gain nothing from doing so, and the cleric only regains a channel divinity.
All in all, I think 5e would have been well served by (a) shorter short rests (5-15 minutes), and (b) more classes having significant resources tied to them. For example, imagine if casters had fewer spells to begin with, but regained one slot of each spell level below their top spell level on a short rest (perhaps maxing out at 5th level – the system seems to draw a line there for other things, like Pact Magic and Arcane Recovery)?