I have another question: Is the DM inclined to inflate DCs to "challenge" or even thwart the character with Expertise?
So, speaking from my PoV... strip out the "thwart" crap and a degree of this will occur in a consistent setting by its very nature and IMO **should not** be something done intentioally "for a character" but rather as the nature of the beast.
In the DMG, it describes assigning Dc and at one point gives what is frankly very close to how i have run "DC" in system after system after system for ages.
it boils down to setting a common pattern based on "who set the challenge up" or "who could be expected to beat it."
the way they describe it -
if neither skill nor aptitude was involved or needed DC10 easy. (A typical inn locks, a typical guy keeping watch, etc.) Average ability scores, no training (proficiency)
If **either* aptitude or training is involved/required - Dc15 moderate. (Innkeeper where they know a thing or two about locks or have had problems that made the hire someone, a "sentry" on watch who has done this job for a while, etc.)
If *both* aptitude and training are involved DC20 hard. (Now if the innkeeper is a former thief or the sentry a skilled hunter as well as exceptional...)
To this i add "resources" that can raise it by 5 for (spent a lot of time or money or has multiple folks doing it) or lower it by 5 for (hard times, not paying guards, not keeping maintenance up on locked rooms or window seals etc)
Now, i suggest that at low levels the nature of campaigns are going to be throwing a lot of "less resourceful" and "less exceptional" and "less well trained and experienced" types of adversaries (as a general rule) and so the DCs produced by the system of "consistent thresholds" will tend to skew low... but as they characters wind up encountering more and more skilled and resourceful and exceptional adversaries as things go on the Dcs will tend more often to be high just because the folks they are opposing have more wherewithal and more resources to apply... parabus etcetera.
Obviously, this will vary with specifics... a giant ogre may not be better at hiding pit traps than a goblin... maybe even worse if the gonblins have more manpower to put to the task. but the general principle can serve as a guide.
The catch is, if the PCs ran up against well-funded, well-skilled inkeeper locks at level 3, it would still be DC20ish. So it is not actually changing the DC to match the party level as much as it is having a consistent way to represent skill, aptitude and resources of adversaries and the challnege they create.
At 11th level, the common inkeeper locks will still be 10s... just there is not much in there "worth having" --- that he knows at least.