It's my contention that the party should feel challenged after each encounter of the day, because each encounter is a test to see if they can keep their resources at or below the expected level for the difficulty of the encounter.
I doubt that's a metric, let alone a sense of challenge that'd resonate with many players...
guideline is there to inform DMs of where the line is, so that when designing a dungeon, they don't make it impossible to get to the end
So, one of the many non-promises Mearls non-committed to in the course of the playtest was 'Crystal Clear Guidance' as to the point, in encounters/day at which 5e was going to balance it's innately-imbalanced collection of classic-feel classes. The 6-8 encounter guideline delivered on it.
At least, I'm willing to give it the benefit of the doubt.
You just need to create days that the PCs have a reasonable belief could have that much XP in them prior to having a chance to rest to get them to use resources appropriately, and thus make individual encounters challenging.
I acknowledge the potential of the living world style, yes, and have made use of it myself.
As for class balance, you are certainly correct that the number of encounters will affect class balance. However, I see nothing in the DMG** that suggests that intended class balance is achieved at ... any particular number of encounters per day. That classes seem balanced to you at 6-8 encounters per day may be a valuable insight gained from your experience,
My experience with AD&D and 3.x was that classes were not mechanically balanceable by pacing, alone, though it could be a significant part of the pressure put on Tier 1 classes in the living world style.
I'm not about to depend on pacing, alone, in 5e, either, but I'm glad to see the guideline.
Because for me, the fact that the game isn't perfectly balanced isn't a bug, it's a feature.
Then it's a feature shared with all games, since perfect balance us impossible.
That does require more work from the DM, but it isn't due to something being designed wrong...
Whether profound imbalance is intentionally designed into a game, as it was with 3es rewards for system mastery, or actively minimized by the design, or as in 5e some sort of compromise allowing the DM to choose dynamic imbalance for it's own sake, or impose a modicum of mechanical balance by adhering to a guidline, it's remotely possible to argue success or failure relative to the intent, but 'right' or 'wrong' is going to be pointlessly subjective.
IMHO, 5e succeeds admirably at delivering the kind of dynamic imbalance that contributed to the distinct feel of the classic game - with some of the more extreme issues and rough edges filed down. But, I have to judge it less successful at the alternative of pacing-imposed mechanical balance, for the same 'elephant' reason this thread has gone over so exhaustively.
It's a near miss, though, and seizing a little flexibility around the rules for resting is a fair solution for an Empowered DM.