To answer the OP. I think they pulled 6-8 encounters out of a hat. Or more likely it came from 4ed. It's been so long since I looked at 4e I couldn't say for sure.
It's funny, there was no solid or explicit guideline for the number of encounters/day in 4e. In one sense, it didn't really need one - the classes had a rough parity in resources, so a shorter or longer day wouldn't greatly disrupt class balance. In another sense, it did, since everyone had dailies, shorter or longer days would make encounters easier or harder - and the dreaded 5MWD was thus still on the table. Eventually, as best as the community could divine from the material, 3-5 encounters/day shook out as a consensus on the intent (an odd number because of how milestones worked). I vaguely remember, sometime leading up to the playtest, perhaps, someone coming out and saying that at release, the intent had been 8-encounter days, and when it became clear that was not the norm, they dialed up monsters a bit in the MM3, and we got to that 3-5 consensus.
Why they'd try to push 8 encounters again (if, indeed, I didn't just imagine it the first time) is beyond me.
From a design perspective if you balance the game by having some abilities available all of the time, some available with an easy recharge (a short rest), and some available with a more difficult recharge (long rest) then you need enough encounters to make those a meaningful difference.
It's more critical when some classes have more of their abilities concentrated in one or the other of those recharge schedules. In 5e, for instance, some classes are mostly at-will with a little short-rest, some more heavily short-rest, and most heavily long-rest-recharge. Thus the 'need' for not only a large number of encounters/day to put meaningful pressure on the classes with many long-rest resources to burn through, but for a rough proportion between short & long rests, and encounters/short-rest.
If you stick to the standard definition of short & long rests, trying to impose balance via time pressure in 5e is extremely constraining to the DM, and can put the DM and some of the players in an adversarial position, in which the DM must find ways to prevent 'premature' resting. But, the Empowered DM can, alternately, simply rule that resting is not possible, take more or less time, or delivers other than the usual benefits depending on the scenario and the situation....
(...heck, I've done that as a dis-empowered 4e DM.)