Ah, we've reach peak Fisking. Was wondering when that would happen.
It is arbitrary. There's nothing to assess. If your argument is that people can make assessments non-arbitrarily, I'll agree, but there has to be something to assess. What you're assessing is arbitrary -- someone made it up. You can lend credibility to an assessment of a made up that to get it from made up (and arbitrary) to non-arbitrary. Doesn't work that way. It's like saying that I have 1 unicorn and 1 unicorn so I have 2 unicorns. I actually have unicorns because I was able to math how many unicorns I have! No, unicorns are still made up, math doesn't save this. Only, this argument is worse because not all assessments are non-arbitrary to begin with, only some, so you're using a statement that's not necessarily true on something made up and claiming it's now non-arbitrary. Dude, just no.
And, for fictional reality, no again. The difference here is just that I describe the wall first, and then make my arbitrary judgement, and then determine the outcome. That's the D&D way -- "there's a cliff (insert description here), DC 15 to climb. <clatter> 16 does it, you're at the top." The other way is to have a fixed arbitrary judgement, determine the outcome, then describe the wall and attempt together. "there's a cliff, so you'll have to do something about it before (whatever reason the cliff is an obstacle happens). Okay, I'll try climb it, <clatter>, um, 7? Sure, the cliff provides some easy handholds, but there's a tricky part that has you execute a jump form one handhold to another. When you do that, you belt pouch snags a rock and rips, spilling coin everywhere down the cliff. You can easily make it the last few feet, but lose 1 coin." Here, at the end of the process, we can't tell one from the other, really. They both present a coherent fictional process and chain of events. So, no, there's not something different in that way. What you're reaching for is the "I like task resolution over conflict resolution," and "I like fortune at the end mechanics rather than fortune in the middle." Valid arguments, but if you're calling what you're calling sim, not ones that actually offset that. You need to work on your definition by way of first principles -- this is sim, and so I can look at game mechanics and evaluate them. What you're doing is saying "this thing I like is sim. But those other things I don't aren't. Because reasons (which shift around as needed to make the argument). Back up and come around at this from a the start with a clear idea of what you want sim to be. And if you aren't goring some of your own sacred cows, you're not doing it right because you're bending to keep your likes on the right side of the line.
I like 5e. But I'll gore it all day long when I analyze it because it is an incoherent mass of crazy. Fun crazy, but not coherent crazy.
The "this part isn't much of a simulation" is, again, arguing over the price. Let's not. The ad/disad analog was a tad bit of a trick, sorry, because that's determined by the outcome of a previous move, which looks just like the one you're tossing out as not sim. Again, sorry, didn't really realize I had done that because I didn't really anticipate your line of argument here. I dislike gotchas in discussion almost as much as in game.
As for the last, yes, they are very much equally arbitrary. You're just restating the argument that if I arbitrarily imaging a thing (or someone else does for me) before an action, that somehow my deciding on a DC for that action with regard to the made up thing reifies it (another great word, which means treating abstract things as real -- hint, this doesn't make them real) into suddenly being objective and non-arbitrary. It's the claim that making it up before is more real than making it up during. It's a pretty BS argument that says that timing is the critical factor in something being arbitrary or not when we're talking about made up things, which are never non-arbitrary.