I disagree with the conclusion. The reason that I use the 6-8 encounters is because there is a large amount of empirical evidence across a lot of tables that shows that this is the point the at-will, short-rest-recharge and long-rest-recharge classes balance against each other as well as common attrition tactics take a toll.
Fewer, harder encounters favor some classes more and disfavor other. Number one common element in "5e is easy mode" threads is that they don't do 6-8 encounters.
BTW, I'm not defending 6-8 encounters - I really enjoy 5e and it's by far my biggest complain about the system. I'm just saying that the reason the 6-8 gets talked about is because not only do they suggest it, but it holds up. Like as if they balanced against it.
The goal of the 6-8 encounters is to exhaust the PCs' available resources. This includes HD from Short Rests & associated Short Rest recuperations that are 1-per-Long-Rest as well as those that recuperate from a Long Rest. So there's 2 or so Short Rests baked into this assumption. One way to deal with this is fewer but more challenging encounters where appropriate. Encounters don't need to be fights, either - they can be traps, puzzles, use of spells to bypass barriers, etc.
Given player agency, there is little control the DM can exert on the execution of the encounters either in which order/manner or whether they manage to get a long rest somewhere in between. Once players start losing a lot of resources they will only push on if there is a powerful reason (i.e. they are --or something they care about is-- doomed if they linger).
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.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.