This discussion highlights a key disfunction in the rules -- how the game explains play vs how people write adventures (especially for commercial ventures!).
The rules make it pretty clear that the DC is decided by the fiction of the moment and the details of the action declaration. A wall's DC to climb is based on the presented fiction of the wall (sheer ice cliff in a thaw sound very challenging) and also how the player's action declaration is formed -- ie, if they try to freeclimb it, that sound nearly impossible, so a high DC is applied (30) whereas if they break out ice crampons and a climbers kit and leave all other gear behind, this make it more manageable and so the DC is maybe just hard (20).
This can't work for published adventures, or in the way many are familiar with adventure prep. Here, the DC needs to be fixed based only on the fiction, with maybe a callout for a change or advantage/disadvantage if the players come up with the anticipated help.
These two things are at odds, and continue to fuel the discussion, because the people that write adventures (perhaps very rightly) feel that if they don't include DCs, people will be upset at having to do that work and it will cost them sales. At home, GMs prepping adventures are conditioned into this approach, and so continue to use it out of comfort and familiarity.
And, to be clear, there's nothing at all wrong with this, or bad about it, or not a 100% valid way to enjoy the hobby. I'm commenting on the tension between how the rules present things and then how it's quite often played (and sold, with regard to official adventures, which also violate encounter guidelines and a few other things).