Yeah, and some of those days will feature less encounters, and favor the long rest based classes (casters and paladins).
On those days, they get a chance to shine.
And some of those days will feature a lot of encounters, and a lot of short rests favoring the Fighters, Monks and Warlocks.
On those days, they get a chance to shine.
Overall balance is maintained.
Understand this point? I've had to make it eight times now.
I'm telling you that the players are actively incentivized not to let that happen. To always keep as few combats between long rests as possible and to avoid taking more than one or two short rests a day.
The big picture is made of small pictures, and the small pictures are significantly harder to control than you are presenting and significantly easier for players to push out of balance.
Or, to put it another way: I'm telling you that for ACTUAL balance of the kind you speak, if you have some days with 2-3 encounters that the casters blow away, you should have on average pretty much the same number of days with
10-13 encounters.* Have you
ever had that happen? Have you ever seen things swing the other direction, where there are way too many encounters for casters to even remotely hope to overwhelm things and the reliability of non-casters becomes an utterly essential thing to keep going?
Because unless you
do, you're saying that it's balanced to let the casters completely dominate some of the time and then to have everyone be more or less equal at other times.
That's not balanced. It just means the casters aren't ruling the roost
all the time. 6-8 encounters puts Fighters and Monks and Barbarians
roughly on an even keel. You'd need to go
even further to actually balance things.
*2-3 encounters is between 3 and 6 fewer than 6-8. Thus, we'd have a theoretical range of 9-14, but that's huge, so I shaved off one from both ends.
Edit: Let me put it another way. You're saying that, on average, things should match up. The "average" day would have 7 encounters. But you're only allowing for stuff up to 8, perhaps 9, while allowing as few as 1. That's going to require a LOT of high-end days to balance out.
For example, let's say that in a 100-day stretch, the party has five one-encounter days, ten two-encounter days, and ten three-encounter days. That would mean 75% of the time, there are more than three encounters per day, surely that is balanced! But we can work out what the average N must be for the remaining 75 days quite easily.
(5+10×2+10×3+75×N)/100 = 7
55+75N = 700
75N = 645
N = 8.6
In order for the average to work out correctly, you need to have more days with 9 encounters than 8 encounters for the entire rest of this 100-adventuring-day span. Even if we drop it to a mere average of 6, the absolute bare minimum, you would need every single day to have 7 or more encounters to make it work out.
And that assumes you as DM have total control over how many encounters players will face. Talk about a "white room" assumption!