It’s not really designed around that number - it’s just that they found out after being mostly done with the design that’s how many “medium” encounters it takes to wear down the pcs. If you stick to “hard” or “deadly” it’s closer to three encounters to wear the pcs down.
Which in more story-driven play styles is still a lot.
It really is though. Or, rather, it's designed around the expectation of a certain number of combat rounds in total between long rests, and deadly (or deadly+) combats struggle to hit that number of rounds without actually killing characters for real.
That's the only way that things like Champion and Berserker can keep up with everyone else. Crits let you roll all damage dice twice and keep the total. Champions get 5% and then 10% extra crit chance. That means, on average, they get that much of their base weapon damage dice as extra damage. Even with the most powerful option (greatsword), that's something like 0.8333... points of extra damage per swing. In order to keep up with the extra damage from Battle Master maneuvers (the
lowest bar to clear, just so that's explicitly stated), you're going to need a minimum number of attack rolls to balance things out. The second crit range increase comes at a level where Superiority Dice are d10s, and the BM gets 6 such dice per short rest. 6×5.5=33 damage. 33/0.8333... = 39.6. At this level, you make three attacks a round as a Fighter, so that means you need a bit more than 13 rounds' worth of attacks to keep up on average, sometimes more. (Note that, because the damage bonus only comes from crits, there's no need to factor in accuracy.)
That's 13 or more combat rounds every short rest. Unless you run incredibly long combats as a rule, that's going to mean about two combats per rest (since long rests also restore things.)
And I haven't even touched on things like Paladin, where if you know you're only getting one short rest most days, you can pump out MUCH more than 33 extra damage per short rest at level 15. Much more, generally speaking, since that baseline Improved Divine Smite has to be factored in. It Eldritch Knight, which gets daily spells instead of short rest Superiority Dice.
So...yeah. The game is balanced around expecting a large number of combat rounds...or else a smaller number of combat rounds and several cases where the spellcasters obviate a non-combat problem instantly
while still keeping up with the (supposedly) super-amazing combat-specialist class.
