I gotta disagree. I don't think there's a huge difference between a rulebook saying "for this specific use case, make it up" and the rulebook saying "for every unspecified use case, just make it up".
I think there's a major difference between "delegating the authority to a participant" and "delegating the authority to a non-participant".
I think that this is interesting, so ... why? This goes back to the Chinese Room (AI) analogy.
What is the difference between the following three scenarios-
1. A coin flip seen by everyone.
2. A coin flip by the DM that only the DM sees.
3. A coin flip by non-participant Jake, who you called, and asked to flip a coin.
I know that emotionally it feels different, and there might be reasons of fairness, transparency, and not bugging Jake to not employ these other methods, but fundamentally they are just outside referents for adjudication.
Actually, for the pure coin-flip game, no one gets to veto a coin-flip. That's a delegation of authority outside of the independent resolution. As soon as you decide to limit the game to particular subset of declarations to enforce genre or setting tropes or anything like that, at least one participant has to become a de facto arbiter.
This is where we get to the whole, "Everyone is playing in good faith" issue that is the necessary background to a system. Let's look at your proposed complete game-
1) There is a player and a DM.
2) The player makes a fictional persona, i.e. a character. The DM explains what is happening to the character, a scene.
3) The player explains what the character is going to attempt, and the result if they succeed. The players then flips a coin.
4) If heads, the player's character succeeds at their attempt and the intended result in realized. The DM then presents a new scene.
5) If tails, the player's character's attempt fails and the DM narrates the consequence of the failure and then presents a new scene.
Under this system, we have a few background assumptions, right?
1. Players can create fiction and there is no "secret information."
2. Every player is responsible for ensuring that (1) they call for coin flips for attempts (as opposed to pure narration), (2) they accurately assign results, and (3) that the results match the fiction.
3. Every DM is responsible for creating the fiction when the player fails, but must do so responsibly.
All of these probably seem self-evident if you are familiar with certain styles of play ... but ... they aren't for everyone. I think that a lot of people would get hung up on some of these - what can players just "do" and what must they attempt by coin flip? What if a player disregards the fiction entirely (the whole bad faith, "I jump over the moon" example)? What if a DM narrates failure that the player doesn't like (you failed at walking 5' forward, so the consequence is ... YOU SPONTANEOUSLY COMBUST AND DIE!!!).
These are background assumptions that are "baked in" to the ruleset you are proposing, and yet they are not self-evident when it comes to adjudication. IMO.