5e expects 6-8 encounters/day, depends on resource attrition over that period to provide challenge, and class balance will fluctuate as you deviate from that guideline.
Why reiterate this?
It doesn't make it right, or good, or fun.
I would never give off advice that leads to a lot of individually boring fights.
A fight where the stakes are "will you have to spend a healing potion, an action surge, a point of ki, or a spell - or will you persevere without spending that resource" is the definition of boring.
Not just because that question in itself isn't particularly exciting, but mainly because a fight where you don't use your kewl abilities is a boring fight where the fighter just whacks away and everyone else uses cantrips.
A fight where already in round one you realize you will probably win the fight (so that you can afford yourself the luxury of asking yourself the above questions; that you seriously contemplate winning the fight without any resource expenditure) must be a completely unchallenging fight by definition.
Even the basic expectation that a fight should take three rounds is something I don't understand. If the fight probably won't take more than three rounds, then the opposition must truly be pathetic.
I can't imagine why anyone would actually give advice that leads to a long series of combats that each take no more than three rounds to resolve, when it would be so very much more fun and exciting to take those monsters and bunch them together into perhaps two fights, that now mean something, that now challenge the players and their characters, where now there are actual risk on the table.
Also; the elephant in the middle of the room that nobody wants to discuss.
In the "recommended" play style, say the idea is for the party to have run out of nearly every resource by their eighth encounter for the day.
This encounter is still just three goblins or whatever; but since the party is all down to single-digit hit points and they only have a few special abilities (like spells) left, now there is actual nerve: will the goblins manage to actually kill off some PCs before the day ends?
But this will never happen in practice. The game is incredibly generous with allowing rests: not only does the game leave it entirely up to the players when to rest and when to retreat; it even supplies nigh-indefeatable spells to facilitate undisturbed rest.
Pressing on when you're incredibly vulnerable for no other reason than the game becomes tense if you do, is an incredibly frustrating thing to ask of your players. Unfun.
And forcing them through story is also incredibly frustrating and unfun - not perhaps once in a blue moon for the sake of variety, but as a regular means of adding challenge.
In the end, the analysis is clear:
I would love a module that's meant as a challenge (like DDO dungeons) where the adventure supplies the restrictions: you know that if you don't reach the end of the dungeon with the resources at hand, you will have failed and will have to try again (roll up new characters and "restart") - there are no rests to be had (or there are rests to be had, but the adventure assumes tight control over where and when you may rest, and sets a hard limit on the number of rests you may take).
Suddenly that three-goblin fight can have actual nerve!
But that doesn't work for general campaigns.
The general solution has to be: since the DM doesn't get to prevent rests, each set-piece encounter has to be challenging enough by its own. D&D is pretty frackin' far from empowering the DM to be able to count on "when they reach the Throne Room they WILL be at half strength, so the Boogie King doesn't have to be overwhelmingly lethal to still present a deadly challenge as appropriate for the adventure finale".
That this leads to fewer encounters between rests is an unfortunate consequence of how stubborn the rules are on "you WILL find rest each night". The DEFAULT is incredibly generous, meaning that the DM must actively harass and wreck the party's resting plans in order to prevent "free" resting.
And I don't like to play the evil stingy DM. I would MUCH rather have the rules tell the players they can't rest. Period. UNLESS the generous loving DM decides from the warmth of his heart to allow it maybe just this once as a personal favor to the players... (Okay maybe overdoing it just a little - but you get my point)
That this favors long-rest classes (like wizard) over short-rest classes (like fighter) is much less of a concern (to me) since 5th edition has shifted the balance of powers rather drastically away from the once-quadratic wizard towards the still-pretty-linear fighter.
What I mean is: with the dearth of save-or-die spells, with the multiple drawbacks of concentration (little to no buffing; only one Big Spell at a time; vulnerability to taking damage etc), and with generally low amounts of spell slots to begin with; no it's not necessarily a problem if adventure days seldom offer as many as six encounters.