I think you missed my rather important distinction between prior to play and during play. The first is given by the rules, while the second is far more practically constrained.
Also, and probably importantly, under section 3 Master of Rules (p 5) the DMG says this: As a referee, the DM acts as a mediator between the rules and the players. The 'rules' there, which I happily grant are whatever the DM decides to use for that campaign or game, quite obviously have weight and function outside the whim of the DM once they hit the table. (Yes, I'll keep using whim because it directly indexes what I'm talking about here). That quote is closely followed by this one: The rules don't account for every possible situation that might arise during a typical D&D session. [...] How you determine the outcome of this action is up to you. It's quite clear that rules are there to be followed (read adjudicated if you like) except when they don't cover something or cause problems. That is the basic expectation of play.
What I'm getting at is that the agency the DM has to change rules is specifically given when it's service to the game, rather than their own whim. The contract and expectations that come along with mediation and the stated goal of create a campaign world that revolves around their actions and decisions, would suggest that the wiggle room for DM authoritarianism over previously agreed-upon rules at the table is enormously more constrained than you seem to want it to be. Just to be clear, I'm not talking about what parts of the rules the DM decides to use prior to play, only DM agency once play has begun and (mostly for what I'm talking about) currently in progress. Once play begins the rules (whatever set is being used) in and of themselves are a significant part of the 'contract' at the table - they are then a set of mutually agreed upon guidelines for the mechanical adjudication of actions.
This whole issue is made somewhat fuzzy here because the 'rules' are not all created equal. Entirely DM facing stuff has far less constraints on change than player facing stuff, and that really describes a spectrum rather than a binary.
As for the last bit, with no social contract you don't have a game, so yeah, the rules need to consider it. How explicitly they do so, or how well or usefully they do so, is an entirely different problem. Personally, I think the D&D rules are crap there, but that's just my opinion.