Combat is just about the only area where a 5E character scales reasonably well, but they're still complete chumps when it comes to climbing a wall or swimming any significant distance. The difference between a level 1 fighter and a level 20 fighter is only +7, which still pales in comparison to the randomness of the d20. That doesn't allow for a good sandbox, where high-level characters get to interact with low-level characters and utterly dominate them due to their inherent superiority. The lies of a powerful sorcerer will still be seen through frequently enough by anyone listening to them, because the fundamental game mechanics are designed to support low-level chumps being nearly as competent as high-level PCs in any area that doesn't involve HP damage.
That's not a good sandbox, if your stats are meaningless because the die is too volatile. D&D 5E is mechanically incapable of supporting a good sandbox, and attempting such a thing will inevitably lead to disappointment. (Which would be forgivable, if the game was only designed to support combat, except combat is also meaningless in 5E.)
To be entirely frank, I don't think your concern is a concern for a significant number of gamers.
A high level 5E character is still so phenomenally ahead of a low-level character that is feels mostly like a theoretical concern (for most gamers).
Sure a low-level character might pull off a DC 20 skill test.
But if the price of failure is falling into 12d6 lava or the Mouth of The Giant Man-Trap there is no real issue in practice since the high-level character will take some damage, kill off anything that moves, and then simply move on. While the low-level character is dead, dead, dead.
I would argue 5E is much better than the editions of old
precisely because you can't just arbitrarily increase DCs to present heroes with the same old challenges, just with "ridiculous difficulty".
That is - I submit the very idea of DC 45 climb checks is borked from the start. The whole point is that you're not supposed to be climbing walls (except automatically, no check required, and in fact without mentioning it at all) no more once you're a high-level hero!
tl;dr: the fact I can (and do) run a complete campaign with only three* DCs** is a
huge benefit for 5E. It might
seem like a trivial small issue, but it really is
very very good!
Z
*) obviously excepting fixed DCs such as a monster's spell save DC
**) I'm using DC 12, DC 15 and DC 20. The reason for not using DC 10 is that is means any and all characters without an actual penalty will auto-succeed by "taking 10" (using their passive score). That is, a "secret door" with a DC 10 to find (don't laugh, I've seen it in official modules) is not a secret door at all, since even a Commoner will find it ten times out of ten!
Make it DC 11 or DC 12, however, and you have a whole new story: you need to
actively roll to find it (unless of course you're actively good at what you do i.e. you have a positive modifier), which means you need to state you're looking etc, you might fail and all sorts of interesting things might happen. Basically, when you go from DC 10 to DC 11
the system starts to work again.
