I'm now asking, for people who average 6-8 per day, how they fit them in a 4-5 hour game session?
I would bet that the answer is "they don't" for the most part. They might spread 6-8 encounters across 2-3 sessions, and have the "day" end somewhere across those sessions. A few people might play more combat heavy games and have 8 encounters in a single session, but I suspect most people do not.
I will speak out as someone for whom this just doesn't work. My regular group doesn't play weekly, and so we like to end our sessions at a "chapter break" (for lack of a better word) to give a sense of closure to the evening's outing. And it's much easier to pick up again with everyone rested when we come back a month later (or longer, given how personal lives have gotten crazier lately) than it is to try to remember exactly where we were resource-wise as well as where we were story-wise. I have very casual players and if the game is making them do too much work to have fun we'll likely end up playing something simpler.
So the way I make this work is that my games are planned as a series of one-shots - I plan them out like convention adventures and work out how they would fit into a 4 hour session. For more dramatic events in the campaign I plan on it being a two-parter where the PCs might get a short rest in between instead of a long one. It means that I might have 2 combat encounters in a session, but those 2 combat encounters are going to be nasty and hard and the equivalent of 4-6 encounters. And usually "important" - I replace the "minor" combat encounters with skill checks where failure might mean a minor loss of hit points and save the combat rules for the big climactic battles. (I also mostly run 13th age these days and that makes doing these things a bit easier, but I retrofit them into the D&D games I'm running when I can).
This has overall made the game more satisfying for my players, but YMMV. I think the "just make sure you're running 6-8 encounters per day" response doesn't take into account how some folks need to run their games and there actually are more knobs to turn with the system than those folks are giving credit for. But you do need to understand the assumption. Another way to "fix" this is to get rid of the idea of "rests" and replace them with "once per battle" for the "short rest" abilities and "once per every 6 battles" for the long rest ones. This is what they advise doing in 13th age for their "daily" abilities and it does work for 5e D&D as well (as well as for 4e D&D - actually it works really well for 4e). This drops the trope of a good night's rest restoring all of your abilities, and it adds a level of tracking that can be annoying to the game, but it's doable and it makes a minimal impact on the rules side of things even if it does make a large impact on the narrative side of what those abilities actually are.