Can you give me an example of "mechanics dictate things sometimes"? That sounds like leakage through that clear line.
Here are two examples:
I am ok with:
"You failed your Wisdom save, so you are subject to the Feared condition. That means you may not move closer to the Dragon, and you suffer Disadvantage on the following checks..."
I am not ok with:
"My NPC outrolled you, so your character finds his argument persuasive and you should act accordingly."
Interesting, I see the former as just mechanical enforcement of "acting accordingly". The PC still has agency to act against the persuasion, but its going to be difficult to succeed going further as a result of it. In the past, I used social checks as a way to hide or distort information from one character to another, but I kinda like the slight mechanical penalty of acting against the result, but not a forbidding of doing so.
In that latter case, here is an example of the player still making decisions:
"Ok, I'm not going to accept that deal."
"The NPC persuaded you, though."
"Oh, yeah, I am TOTALLY persuaded. But I'm also a little scatter-brained so I forgot all about it and now I'm focused on this other thing..."
This is one area I never approach. I never use a social skill to force anything. Whether that is an NPC
or a PC. I know some folks believe that a PC can persuade check an NPC into some action, but that doesn't also work the other way around on PCs. For me its a different approach altogether.
I know some folks refer to it as social combat, i dont necessarily like the term, I might prefer something like social encounter instead. Though, lets use an example of agreeing to a deal. An NPC might be standoffish and ready to walk. The persuade check isnt to change his mind and force him to agree to the deal. The persuade check is to bring them back to the table and open them up to the possibility. The roll matters becasue failure means no deal in the short term. The negotiation continues with a successful result. Then, new parameters are set and you keep working towards the goal; like rounds of a combat.
If that is acceptable within the definition you offered then, yeah, I'm ok with that. But in that case I also don't understand the point of even saying that the PC was persuaded. I'll also point out that if the goal is to prevent players from 'making their characters immune to influence' it does nothing to accomplish that, and encourages players to be deceitful at the table (which in general is one of my concerns about attempts to control metagaming.)
For me the metagaming aspect isnt something I try to control, I just dont accept ignoring it completely. For example, our lose weight and eat cheesecake example. A player might choose the weight loss goal for their PC. Then, despite hunger pains, temptation, peer pressure, etc.. they simply have the character subsist on water and saltine crackers for 90 days to reach the goal ignoring everything in the millileu. Its wooden, its stale, its an uninteresting approach to reach a goal for the goal sake itself. The journey is always more interesting than the destination. YMMV