I can understand where you are coming from, but I don't agree.
There are plenty of places where roleplaying happens with no mechanical impact; interactions between characters as they get to know someone, dialog for a romantic scene with an npc that is done without dice rolls (just as a way to enjoy experiencing the conversation) as a couple of example. There are lots of situations where you just interact by roleplaying that have no stakes, and have no need for a mechanic widget tied to it.
I think I might already have quoted
Chrisotpher Kubasik's Interactive Toolkit in this thread, but I'll do so again, because it expresses where I'm coming from fairly well:
The tales of a story entertainment [his term for a RPG] are based not on the success of actions, but on the choice of actions; not the manipulation of rules, but the manipulation of narrative tools.
The primary tool is Character. Characters drive the narrative of all stories. However, many people mistake character for characterization.
Characterization is the look of a character, the description of his voice, the quirks of habit. Characterization creates the concrete detail of a character through the use of sensory detail and exposition. By "seeing" how a character looks, how he picks up his wine glass, by knowing he has a love of fine tobacco, the character becomes concrete to our imagination, even while remaining nothing more than black ink upon a white page.
But a person thus described is not a character. A character must do.
Character is action.
I would depart from his contrast between "rules" and "narrative tools" - "narrative tools" are a form of RPG mechanic, though they may not always take the more-or-less-sim form that Kubasik has in mind in dismissing "rules". But the idea that the character reveals him-/herself through action - which in a RPG means action declaration - is something I agree with.
I would generally not expect to spend time at the RPG table listening to conversation for the sake of it. Even experienced fiction authors and film makers don't always pull this off, and no one at my table fits those descriptions! If a PC was getting to know someone by way of romantic dialogue, I would expect a reasonably brief description of what the conversation or flirting or whatever consists in, and would then resolve the situation (perhaps "say 'yes'", or alternatively calling for a check to see how the NPC responds).
Two concrete examples that illustrate how I would normally expect this to be handled: in one of my RM campaigns, the PCs rescued a NPC sorcerer from captivity by a demon. One of the PCs wanted to woo this rescued person. He already had Amiability developed to a reasonable degree, but was worried about them becoming "just friends", and so developed Seduction skill - the nearest skill on the skill list we were using to a wooing skill. The actual resolution I think mostly took the form of "saying 'yes"' - it's 10+ years ago now and so details are hazy in my memory - given that it made sense for what the character was attempting and how things were unfolding. The wooing was not played out in much detail, but what was important was that they were able to found a dynasty that was to be responsible for guarding a gate against otherworldly intrusion - this was narrated as part of the endgame, but consolidated a campaign-long established contrast between this PC and his cousin, who was more valiant and capable in immediate action, but had less of a long term stalwart character to him.
A recent example is in my Prince Valiant game, where two PCs are competing for the attention and affection of Violette, the daughter of a noblewoman whom they helped avoid (what would have been) an unhappy forced marriage following the death of her husband (Violette's father). In this context, I've taken it for granted that Violette might be attracted to either, and have been framing mostly as competitions between the two PCs (which so far have all been tied, indicating that Violette has declined to make a choice, and that neither PC has agreed to yield to the other). But one PC (played by the same player as in the previous anecdote) just developed Courtesie skill to give him a better chance at wooing Violette - it hasn't yet come into play, though, as they are out on deeds of errantry.
Those are examples within the context of PC/NPC romance where I see mechanics and RP as the same thing.