A weird thing about monsters

[Darth Credence]

I don't see how it's not by far the most meaningful thing. If you do not at least stay level re: success rate while fighting "fair" encounters at various levels, that means your character is getting worse at things. And while an argument can be made that it's fair for the character to fall behind in things they do not invest into (a non-proficient save with a non-preferred stat), I would not understand why a proficient save coupled with a preferred stat (i.e. something that gains the most increases overall) does not only improve against "fair" enemies, but actually gets worse.

It does not mean your character is getting worse at things, at all. It means things get harder. The characters are clearly better - the fighter went from a 60% success rate to an 80% success rate against the basilisk. A wizard would get a similar increase for wisdom or intelligence saves. There is a big difference between getting worse and facing more difficult challenges.

These criteria are useless, because they are basically asking "do high levels have the capacity to get bigger numbers than lower levels? if yes, it works as it should". Of course they do, it's what levels are there for.

Yes, that's what levels are there for. That's my point. As one goes up in level, they get better at the same task if they work to get better at that task, as abstracted by the improvements associated with it.

Because the level 20 character is basically a dragonslaying demigod who can, with their jolly band of three other people, quite positively slaughter a couple of somewhat lesser dragons (like adult ones) before breakfast. Meanwhile a basilisk is a terrifying beast for some Joe who basically picked up a sword, trained with it for a few months, then put on his grandpa's rusty chainmail and set off to have an adventure.

See what I mean? These are fluff descriptions one can twist in any direction they wish. Mechanically, this makes no sense, and that's what's important.

Mechanically it makes perfect sense. A level 20 character is very, very good at what they are good at. They are no better at what they are not good at than they were when they started if they did not put any effort into getting better.

Should all level 20 characters be good at casting spells? I mean, they're dragon-slaying demigods, after all, so they should all be able to throw fireballs around at will right? Or, the casters get much better at casting, and the martials get much better at fighting, because that's what they concentrate on. Saying that everyone should improve all saves from how they started is really no different than saying all characters should improve their ability to cast spells above where they started, or all characters should improve the number of times they can attack per round from where they started. It's just more obviously ridiculous when we talk about those things that are specific to the class.

Well, saving throws are also specific to the class. A wizard gets more damage out of cantrips, access to higher-level spells, and more slots as they get better at magic. They also, by dint of being wizards, get better at resisting effects that target their wisdom or intelligence. A fighter gets more attacks per round, better stats, and the ability to surge for a bonus action as they go up in levels. They also become more resistant to things that target their strength and constitution. Those improvements to saves for both classes are every bit as much a feature of the classes as anything else, and the expected improvements for someone following that class.

Want better saves? Spend some training time to get them. A fighter gets 7 ASIs or feats over their career. A wizard gets 5. Those five would be enough for the wizard to become proficient in every save type, which would also bump their ability scores in everything not wis or int by 1, and have one left over. Or, if you are worried specifically about one falling behind, the fighter mentioned could get their ability to save against the green dragon breath up to 50%, and be better at that than a normal person is against a basilisk. But these are all choices that have to be made. If someone wants to change their game so that everyone just gets better at all saves, thus invalidating these kinds of choices, they certainly can, of course. But the idea that saves are broken because in a normal game, there is a cost to be able to save against a high CR creature as easily as against a low CR creature is just wrong to me.