That's the idea, yes. You can achieve balance over a long term, by balancing short-term imbalances. It's, well, a balancing act. You have a massive single encounter where sort of character shines, you 'balance' it with a long slog where that same sort languishes.
Imposing that kind of balance does "limit" how the campaign can be run - a better way of putting it is that it makes establishing and maintaining balance a constant consideration for the GM, that has to be, well, ahem, balanced with other considerations in plotting his campaign...
What constitutes a 'right' or 'wrong' choice in terms of balance depends on the PoV and objectives of the ones making the choice. A 'right choice' in optimizing a party to defeat enemies in 3.0, for instance, was scry/buff/teleport, it's radically imbalanced, but it achieves the objective. 'CaW' style play gravitates towards badly-balanced systems for that reason. In-game and meta-game decisions can create wild swings in effectiveness relative to the challenges presented, raising the significance of 'player skill' in gaming the system.
They're just guidelines, and they work over a limited range. I didn't mean to imply that you couldn't operate outside that range, just that the guidelines stop being very helpful when you do. Considering how long many of us designed & ran encounters with no guidelines at all, that's obviously an issue that can be dealt with.

But, if you do want to be able to 'trust' encounter design guidelines, if you do want to impose some rough balance on classes without micromanaging challenges to give each PC is ration of spotlight time more or less arbitrarily, then you can run the game at the pacing it's calibrated to. Either of those options limit you as a 'storyteller.' You can use such limitations as a source of inspiration, of course - a blank page with no assumptions can be a downright intimidating place to start, anyway.
Again, "sameness" is not a synonym for 'balance.' Indeed, it's arguably antithetical, since, in the absence of choice, there is nothing to balance. You can differentiate two choices by means other than making one superior to the other.
And, yes, since D&D was the first RPG, and was 'balanced' over the whole campaign (and probably many characters played by each player in the process), that's a foundational way of providing balance. That doesn't make it the only, or best, or adequate, or even a good way of achieving balance. But, it is a method of imposing balance that requires the GM to make decisions about the campaign with the purpose of making balance happen.
More robust balancing mechanisms can reduce or all but remove imposing or maintaining intraparty (class in D&D) balance as a consideration the GM has to work into his campaign. That's what makes using spotlight or pacing to impose balance seem 'limiting.'
Yes, I am. There's no question there's an impact, but minimizing it isn't going much beyond what DMs do just as a matter of course running the game, in the first place.
All 5e classes cast spells, and most of them cast spells as a daily resource, so you're really down to sub-classes. Roughly:
Short-Rest-heavy: Warlock, Monk, BM.
Long-Rest-Heavy: Cleric, Druid, Wizard, Sorcerer, Bard
At-will heavy: Thief, Assassin, Champion.
At-will & long-rest heavy: Paladin, EK, AT, Ranger, Barbarian.
Nod, that includes all the primary casters, the half/third casters who can stack their long-rest abilities with their solid at-will baseline, and the Barbarian (which does likewise in a big way with Rage). That's Barbarian, Bard, Cleric, Druid, Paladin, Ranger, Sorcerer, & Wizard plus EK & AT - /most/ of the classes in the PH. It would be no effort or hardship, at all, to have a party made up entirely of members of those classes (and sub-classes). The Warlock also does just fine in the scenario, since it's short-rest resources /are/ the same spells as the other's long-rest slots, and it gets to recharge them after every encounter, and the Monk & Battlemaster aren't far behind for the sane reasons.
So, really, it's the Champion, Thief & Assassin out in the cold. Just drop them from campaigns that are going to use the 3-4 trans-deadly encounter/2-3 short rest 'day' as the average. No big loss.