Certainly a lot of people who don’t like the 6-8 encounter adventuring day guideline seem to think that those who do are “treating it as holy writ.” The truth, however, if you look closely at the game’s math, is that the 6-8 encounter adventuring day is simply an underlying assumption the designers used to balance the math. Just like starting with a 16 in your primary ability and increasing to 18 and 20 at levels 4 and 8, just like getting +1, +2, and +3 weapons at levels 5, 11, and 17. None of these things are requirements. The game runs fine even if you don’t follow any of these guidelines. They’re just the assumptions the system math is built around.
I wouldn't call them assumptions, rather an expected average.
I mean, from level 1, the math actually is extremely...off ran the way its said its expected.
A medium encounter from the game at level 1 would be a single encounter bugbear.
Now, I'm not sure if you've ever played through LMoP, but there's an infamous bugbear that definitely DOES NOT feel like a "medium" encounter. Many PCs have fallen due to his impressive 11 average damage against PCs whose health is around 7-13. Meaning he can take out a single PC in a single hit, crits notwithstanding.
Now, imagine a party of level 1 players having to run through 6 of these bugbear encounters and you'd probably TPK after the 3rd one, even with a paladin, cleric, or bard amongst them.
And going higher, at level 10, a medium encounter involves 2 Young White Dragons. Are you certain that an average party can really expect to be fine after 6 of those fights?
Because by my calculations, if the dragons get only their first turn in a round, they can do enough burst damage to take out a cleric's 63 HP and turn what should have been "medium" by calculation into actually deadly basically immediately.
And this is assuming the party was topped off. If the party was in a position where their 5th and 4th level slots are exhausted (basically the 3rd fight in a day), the party is going to have an even harder time and the danger has only remained the same.
I still think the 6-8 encounters is a ceiling for the average player. Sure, a party of optimizers might be able to survive or even surpass this, but I don't believe the game is designed around the hardcore fans.