Disintegrate isn't an all-or-nothing effect, just a source of damage. (In 5E... that too is a "modern" change, IIRC between 3.0 and 3.5. The old disintegrate was save-or-die.)
Point is that D&D characters get more resistant to magic as they level, as a matter of course, just as they get more resistant to injury. Thus "it's magical" is no excuse for 20th level character being scared of a 3rd level mummy.
Well, it usually won't, because 20th level characters would tend to have higher ability scores and be much more likely to have defensive magic items/abilities/effects.
Not nearly true enough. You have 6 ability scores, at least one of which will be a high priority for your class, and only so many ASIs. Even a character who does spread his ASIs out to include even his lowest-priority stats will end up improving each of his saves very little over 20 levels.
Except that part of the point of having all-or-nothing save effects (as opposed to save-for-half-damage effects like dragon breath and fireball) in the game is that having higher HP doesn't help against them.
That's a reality of it. It's also a reality of the mechanic that it doesn't matter if you're injured, too. The point is probably more that the condition doesn't involve killing you, and doesn't have a an intermediary state - not that level shouldn't matter, merely that hps aren't the target of the effect.
Well, I have the most background pre-5E with 3E/3.5/Pathfinder, so that might influence my take too.
3.5 is when they introduced 'bad' saves and made it possible to cheese up untouchable DCs, even when good saves were involved. It tilted things wildly in the favor of casters in a lot of ways, relative to both the classic game that preceded it, and the edition that followed.
And I'm not saying your position is wrong - but I don't think the way saves work in 5E is a designers' math error
I don't think it is, either. I think it was a conscious decision, just a bad one.
One strength of 5e, in that regard, is that it's easy enough for me to correct as a DM.
I lean towards giving non-proficient saves a lower proficiency bonus instead of none at all. Prof-2, so 0 at 1st level, going up by +4 over 20 levels.
When I first picked up 5E, I was quite disappointed that the super scary effects of editions before 4E were mostly missing, but now I think it works well overall with the new mechanics.
They're not missing, they're just not implemented the same way. Same was true in 4e. Medusas could still turn you to stone, Beholder Death Rays still kill you, just not via a single bad roll or bad save.