On the other hand, skill bonuses that are high lead to trivial challenges. A DC 20 may not change, but it's importance as a factor does. If you can beat a DC 20 on a 1 (not out of the realm of possibility with expertise, high stat, and magic*), why bother having those DCs?
Here's the rub, if a player has a very high skill, one that is only challenged by very high DCs, it starts to fade into the background. The player, perversely, loses spotlight time due to their specialization. If, as a DM, I know the player can autosucceed at DC 15s, and is unlikely to fail at DC20s, then I start glossing them in play. "The door is locked." "I attempt to pick the lock." "(no roll needed, autosucceed at the DC)Sure, you pick it, what now?" This removes that tension of picking up the dice to answer the question 'can I pick the lock?' and replaces it with rote narration. I'd rather a mechanic that let my player, the renowned thief, still have a bit of a thrill at picking a lock without the lock being an unreasonable and unsupported by fictional positioning super high DC.
Heck, replacing the double skill bonus with advantage would be better. Then it's still a risk.