Yeah, going "Hey, wanna dance?" and immediately getting "Ew, get away creep!" is the kinda shit that only makes sense if you're trying to roleplay off a natural 1 on persuasion, a near 0 charisma or some weird/asshole character quirk.

Otherwise a simple yeah/nah makes way more sense as someone who isn't a nutjob forcing their own narrative against the rolls.

Indeed. A 20 on the roll means that circumstances beyond the usual line up to result in markedly better performance, even if there is no "critical success". How this is approached is up to the DM and players present. Perhaps some aspect of the gent reminded her of a childhoood crush or a folk hero's appearance, or his straightforward approach happened to be narratively what she was looking for. But the character themselves is not declaring a dice roll and victory, as that is not a seduction check, unless, again, narratively that WOULD HAVE BEEN one, say for example you're in a temple dedicated to a god of gambling and whoring in which case such a statement perhaps COULD be an attempt at seduction.

You don't say "I attempt to hit the dragon with my sword" and then roll a swimming check followed by a contested herbology check. The skill check has to relate to the action performed.

DC checks, while they are random at times, should be comparable to others in the same range. Let's assume this nerd's got literally zero game: net 0 modifiers. In 5e, what is a DC21+ skill check? The Guide says it should be particularly hard, even for someone who is trained and skilled in the thing being tested. They give the example of hearing an animal that is hiding silently. Another example would be dodging an elite archmage's carefully aimed Fireball. Compare the skill required to do those, the time taken to learn how, and how much time and effort you would need to be a passing pick-up-artist.

"Roll for seduction" can have high DCs: Say the person literally has no interest in anything sexual for some reason. But that is no reason for the DM to deny the roll. D&D is improv, the answer should always be "yes" or "yes, but...". The uninterested person becomes enamored with the roller, even if not physically. They find your attempt funny, and raise friendliness rating two ranks. It isn't mind-control, but the job of the DM is to find a way to make the effort reward the player. They're engaged and faithful? They know a friend who'd like to meet you. They're restricted in their actions or have impossible standards? They set forward those standards in clear language, ideally as a plot hook ("My father will only let me give my chastity to someone who can refurbish the haunted mill, you see... I've been trying to figure out how to do it myself, I can share with you what I've learned" or whatever).