iserith
Magic Wordsmith
We seem to be on the same page, but you are I think being biased by that perception and so assuming both that all GMs run their game that way, all game systems encourage that view point, and that all players prefer it. I don't believe that is the case.
Please bear in mind I am speaking solely of D&D 5e and, in particular, a challenge that was presented in my game. I might argue differently if we were talking about D&D 4e or someone else's game. That said, I cleave to the rules and processes of D&D 5e quite closely and I think to some extent any DM who does the same is likely to reach the same conclusion. I make no judgment here about what players prefer, only what are usually optimal decisions in this paradigm (avoiding the d20, for example).
It's possible to run this challenge you've described using a only flow chart which at every branching point features, "Character failed or succeeded?" and never branches on player choice at all, and I think some GMs lean very strongly to preferring that process of play. If I used such a flow chart, this would be entirely a character challenge, and even if it wasn't a pure character challenge because a few trivial decision points for the player remained, it would still be close enough to a pure character challenge that I wouldn't feel amiss calling it a "character challenge".
I would likely call it "random number generation." The important choices were made at character creation/advancement, short of the few trivial decision points you mention.
Some games, at least as written in the rule book, have a process of play where every player proposition ALWAYS is mapped to a particular rules proposition which calls for a fortune test, and for each proposition offered to the GM, the GM's role is to interpret correctly which rules proposition the player actually made. I've even read rule books where it called out that if the player made a natural language proposition, and it was unclear which rules proposition - which character 'move' - the player was making, that the GM should invalidate the natural language proposition and force the player to phrase the proposition as a rules proposition.
Dungeon World is something like this, where a fictional offer made by the player is judged as to whether it "triggers" a move and that both the GM and players are tasked with making sure that moves are used when appropriate. Most but not all moves require a die roll. That's a different kettle of fish for sure than D&D. (And I really like that game, for different reasons. I was a playtester for it as well.)