Yes, I was imprecise, I meant that you get more and higher slots with caster level, not the caster level directly affects slotted spells. I would have combined caster level stand in for level in cantrips, though. Otherwise, cantrips just get better for no clear reason, while everything else requires you to become a better caster to have more effect.
They'd be exactly the same, whether by the RAI or by my houserule.
I don't think I buy this analysis, because that's how everything else works. You don't have to keep practicing combat skills for your proficiency bonus to increase. Or any other skills. You get better at all the things you Can Do At All through levels. I mean, your first level spells may not increase in damage done, because you don't have higher level slots, but their save DCs go up anyway. Everything increases with proficiency. If you take a single level of barbarian, then spend the rest of your levels on wizard, it's still your barbarian con save that gets the +6 proficiency bonus at level 20.
So in
general, 5e's model is that you don't get better at specific things because you're levelling in their class, but that class levels give you proficiencies or abilities, and then you improve at
all of the things you're able to do as you level.
So I don't think cantrips getting better is any kind of exception; I think it's the general rule. A fighter 1/wizard 19 gets the same +6 to hit with a martial weapon that a fighter 20 gets. So I don't think it's unusual or contrary to how everything else works; I'd argue that if you want to keep cantrips from scaling for multiclassed characters (or people who took a feat), you should probably also do the same thing to things like save bonuses, applying proficiency bonus to particular skills or weapons, and so on. And I think the reason the system isn't like that is that that keeping track of that kind of thing was a lot of hassle. It was sort of justified in 3E because the intent was to have that broad a range... But bounded accuracy is a
fix to the problem that resulted from that.
And if you accept bounded accuracy, the increase in cantrip effect with character level, rather than class level, turns out to be logically implied.