I think perhaps it would be better to have two separate level-based DCs. One for things that are supposed to be "challenging" and that demand specialization, and one for more "routine" things. Things like Repair, Recall Knowledge, and so on could be on the "routine" track instead, which would keep characters from feeling more stupid at higher levels because their effective skills have narrowed too much.
I've heard people wanting to use the Simple DCs as a basis for things like Recall Knowledge, basing it on their rarity rather than level, and that's probably a smart way to do things; even if something is high CR if it's fairly common then you'll be likely to know something about it. Given that those Knowledge checks are going to be spread around different skills, having them still achievable by people who may not have taken the skill would be worthwhile simply because a Blue Dragon is still a Blue Dragon and they've likely heard something about it once. But that's also a good instance where even more gradations of successes might be good: beating a check by multiple levels could yield more exact information or more questions to ask the GM. You could even list different things to ask like Free League knowledge skills typically do.