The high level spells (mystic arcanum), I perfectly understand why those slots are once a day, not once per short rest. The balance reason is obvious.
What I don't understand is why these slots are restricted to a single spell! As noted above, this is quite restrictive and I don't understand why.
I'm pretty sure the answer is that the class was designed late into the production process, and they had to try and fit different ideas into the mechanical language which had evolved to accommodate the core classes. They were able to make the basic pact spell slots fit into the short rest mechanic by severely limiting spell access and only giving out 2-3 spell slots at a time, but that didn't translate well for the higher-level spells that were already limited to one slot per day.
As awkward as it is to know only
one level 6 spell, the alternative would be
more awkward. Where a Sorcerer can know a couple of level 6 spells, they can at least (theoretically) cast those in higher level slots, so they might actually end up casting two or three different level 6 spells in the same day; and that warrants
knowing at least two or three level 6 spells.
Contrast with the Warlock, where the unifying theme of all their different spell mechanics is that you never have to
decide which spell slot to cast a spell from - rituals are cast at their minimum level, cantrips scale automatically, a low-level spell is always cast at the level of your pact slots, and a high-level spell is cast at exactly the level of its Mystic Arcanum. If you think about Warlock as being the "simple" spellcaster, which was one of the original design goals, then it's actually pretty noob-friendly to
not have to make that decision with every spell you cast.
But the point where I was going with all that is that it would be kind of awkward if they let you
know three different level 6 spells, and then gave you exactly
one spell slot to split between them, and no way to ever cast more than one of those per day. It's a resource-management puzzle beyond the scope of what any other class has to deal with, so it's not something they wanted for their "simple" spellcaster. (And if they allowed upranking of a level 6 spell into your level 8 slot, or whatever, then it would raise the complexity of the class as a whole.)