Obviously I disagree

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Yeah I figured lol
But it’s not farcical. How can you point to a system and claim that that system is doing something when that system isn’t actually being used?
I wouldn't, we just have different perspectives on what constitutes "use".
Put it this way. I’m trying to talk past a guard. I talk to the dm and we play it out, no dice, and the guard lets me pass.
What game am I playing? Am I playing DnD or Vampire or Fate or Chivalry and Sorcery?
Try a scenario with high enough stakes that any game would bother engaging the mechanics, and the answer changes. And certainly, even here, there are games we could cross off the list.
Since it could be any of the above, how can you claim that one game is supporting this?
You could describe an actual skill check due to a more recalcitrant guard, and depending on how closely you hew to the linguistic style of a given game, it could be quite difficult to tell.
Now, other systems than DnD will have mechanical frameworks to resolve this. But DnD doesn’t. So again how do you claim that DnD supports this as much as or more than other systems?
But DnD does have a mechanical framework to resolve the situation. You've chosen a scenario in which many GMs wouldn't engage the mechanics regardless of the game. I'll use a more appropriate scenario.
Well, same scenario, different guard, higher stakes (for both the PC and the guard).
You approach the guard, clearly intending to pass through.
Let's say you want to try the "walk like you belong" trick. You describe your approach to the GM, and they think about what the guard is guarding, how much they care about their job, etc, and decide that this is possible, but not likely.
Now, if it's me, I tell the player roughly what their chances are, but not everyone likes that.
So you roll. Certainly Charisma, probably Deception, but literally any charisma skill could make sense in this specific instance. Let's say you roll poorly, to keep the scenario going rather than just bypass it in one.
Now, the guard challenges you, like he's supposed to. What do you do next?
Right off the dome, you could ask if you can discern anything about the guard that will help you decide on the best tact for getting past him, you could jump right to charming, intimidating, appealing to his moral nature, etc, you could use a deceptive manner to get close enough to knock him out. You could, I suppose, run and try to sneak past later.
All of those are likely to require an ability check. Using ability checks in 5e dnd is a conversational rules system. Other systems may have a conversational element, without using conversation to resolve the fictional events.
So, clearly, the game supports solving things nonviolently, using the rules. But lets say you for some reason think that low stakes resolution is required for the game to not be "mostly combat". (let us be honest, here, and note that this requirement would be absolutely bug circus on a hamster wheel silly)
We can go back to your first example. The GM almost certainly considered using a check to resolve the moment, and chose not to based on your roleplaying. So, you described an approach with no reasonable chance of failure, and the GM didn't arbitrarily make you roll anyway. Okay. Because 5e's resolution is mostly not strictly prescribed, figuring out to what degree to use any given mechanics, how much to zoom in on this scene in terms of how complex a challenge it should be, is all a conversation, but you aren't "not using the rules", and even if you weren't using the rules...the fact that you can resolve low stakes situations without the mechanics doesn't mean that those mechanics don't exist.
The real problem comes in when you talk about all of this with language that very much comes across as telling people who prefer the social pillar to function this way that they don't know what they're talking about, or that their perception of what they're doing is false.