I think again you are missing my point.
I'm not saying that theDM chooses a different DC for each PC.
I am saying that the DMG doesn't inform you of what DV means in a arrucate way the DM can understand or use. In it does thinks a confusing way by framing it in the hands of a character with a 10 even through most Players won't have many 10s in 5e and will avoid actions that use a ability score with a 10.
And I'm saying DMs don't have to know a great deal about the underlying math because DCs are pretty constrained in this version of the game, which actually makes it more approachable. Pick 10, 15, or 20 and move on.
And what world is a 75% failure chance Moderate and 50% Easy? Even under stress, I wouldn't call anything I can fail half the time at EASY.
You seem to be undermining your previous criticism about framing the guidance with a character with a 10 ability score. If you are correct in your assertion that "most players won't have many 10s in 5e and will avoid actions that use an ability score with a 10," which is somewhat reasonable, then it actually
will be Easy, relatively speaking, since characters will have higher scores than 10 and/or will tend to focus on those related tasks (as you say). So that 50% chance of failure drops. Also, don't forget advantage, plus other bonuses players can apply to further increase the odds of success. Clearly, the DMG is just trying to get DMs a ballpark idea of what the odds are, given certain assumptions, rather than a primer on probability and statistics.
So you end up with a situation where the DMG becomes Anti-DM because frankly many veteran DMs don't like being told what to do and thus frown upon giving new DMs clear rules in case the advice given is contradictory to how they themselves play.
And thus page 238 ends up not being actually useful for anything but the permission to make stuff up and not take the blame when the mechanics don't match the fantasy like editions before it.
I'm not sure how you leap to "the DMG becomes Anti-DM" or how that relates at all to many veteran DMs "don't like being told what to do."
I'm a veteran DM, and I
do like being told what to do. And what the DMG tells me is that picking 10, 15, and 20 is just fine -
so I do that, and it actually works!
It is good to see, however, something of an admission that your thinking on this matter appears to be influenced by previous editions. I still run and play D&D 4e. I don't run and play it the same way as D&D 5e. That would not be a good idea in my view, nor is carrying one's expectations about how one game works into another game. They're not the same thing, so thinking about it the same way is not productive in my experience.