Doesn't that require consistency and transparency, as afforded by a set of specific DCs for actions?
It requires a good degree of consistency within the campaign - yes.
i consider it a intentional goal of mine to apply a fairly consistent set of Dcs, derived from the basics outlined in the DMG and the concept of "who could do this reasonably" or "who set the challenge up."
if the answer is "not skilled at it and not exceptionally adept (non-proficient and no ability score boost) the DC is 10
if the answer is "either skilled or adept but not both" (either proficient or ability boost but not both) the DC is 15.
If the answer is "skilled and adept both" the answer is 20.
After that the question becomes one of resources:
if the circumstances are such that extra resources were brought to bear on the "setup" or necessary resources are absent that are needed the DC gets worse up to 25. An example would be a wealthy sort who hired very very good security and gave them lots of resources due to being paranoid.
if the circumstances are the reverse - maybe a tightward who after hiring a good firm cut back and underpiad them etc... or the money dried up so upkeep did not keep going... DC can drop by 5 down to 5
They key is you do not need pre-set book provided laundry list of generic DCs for pre-defined tasks - you need a consitent set of standards that can be used over and over again.
Obviously when you hit cases of direct and active opposition the idea of "who vs who" becomes more obvious but the same sort of principle is more or less imbedded in the DMG recommendations that include the 10-15-20 are fine bits etc.
For example, i could not answer the question of the DC for a 20' standing jump cuz a lot of things matter including the strength of the jumper (to give me an idea of what his default minimum would be so i know how "unusually long" this jump is.)
But thats how i run it and so far it has worked great. My players and i seem on the same page the vast majority of the time and they make informed decisions and have no problem accepting a variety of outcomes.
But, my advice for a GM who has issues between his players and himself over skill DCs would be two-fold - first try and be consistent and let your basic prinicple be established publically session zero and Second consider the PHB "progress with setback" reference from the PHB as to what a failed skill check is very carefully and realize you have a very wide lattitude even if you do not go as far as the "success at cost" and other minimal success type options in the DMG.
I find reasonable process for assigning DCs (as they provided) much better than scads upon scads of pre-fabbed lists of Dcs that may or may not apply.
EDIT TO ADD: By the way, a side benefit of this is when the PCs in an otherwise ratty scale inn find a chest with a DC25 lock they cannot pick - its a clue they pick up on that something is not as it should be, something is out of place, etc. thats part of the advantage of a campaign where consistency and informed decisions are common - outstanding elements are features not bugs. its a cue to me the Gm to describe things a certain way and for PCs to question the whys and wherefores of whats going on.