I freely admit that i'm much more happy with a social meeting and/or interaction being reliant on the players words and arguments than mechanisms, even if the roleplaying involved is 'translated' into a modifier to the eventual dice roll. Instead of relying on the vagaries of a dice roll and the decision of what modifier to apply to it, i like to think of social interaction as a puzzle much like one encountered in a dungeon.

You approach your goal and find that a complex mechanism bars your progress, you search for levers, pulleys or wires that you can manipulate to disarm the trap or reduce the difficulty of the puzzle. You then push this lever to gain your desired result, continuing until the puzzle is solved.

Each diplomatic or social encounter can be reduced to: state desired result, search for an angle, exploit that angle, once the door is open walk through and claim your prize.

Example: Prince Radar is lord of the marches, the PCs want permission to search his lands for the mythical ruins of Mandragor, however, the Prince is on a war footing and doesn't allow people to wander willy nilly for fear of spies. His secret police are everywhere and he is paranoid in the extreme. He will be a tough nut to crack.

Stated desire: Permission to search for Mandragor
Search for an angle: The PCs talk to the Prince about the current war, sympathising with his troubles, but still pressing for permission. The Princes paranoia becomes apparent after a while.
Exploit the angle: The PCs tell the Prince that legend tells of a mystical item within the ruins that can tell if a man is lying. They will give this to the Prince if he gives them permission to search. The PCs are lying, but they have gained permission by determining the correct angle to exploit. The consequences may turn out to be nasty, but that's a problem for another day and gives ideas for further scenarios.
Success!

I wonder if social encounters could be 'statted out' in a manner similar to this so as to exclude blind luck (with some exceptions). Then each social encounter becomes similar to a puzzle found within a dungeon that the PCs may be exploring. I'm not sure whether i'm stating the obvious here or whether reams of character profiles could be distilled into a 'social stat line' like that proposed above.

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That's a good way to codify it, but the Prince might give permission in exchange for hot sex too.

I don't think we need to codify it. It turns out that it's fun to just play it out and see what happens. The only thing that needs a little protection is that if the players fuck up massively they should at least get a roll or two to escape from the situation. Other than that, it's just playing make believe. Which is really fun.

A good adventure should discuss NPC motives in their profiles, IMO. Whether it's qualitative description or codified conditions, it doesn't matter much to me. You could list 'fear of spies +20', or you could simply describe the Prince's fear of spies in his background blurb and leave the mechanical details up to the GM.

I do think that PCs should be allowed multiple avenues of success to winning social conflicts with any given NPC, some of which are more effective than others. I wouldn't mind seeing NPC motives listed in bullet format though, distinct from personality/background/physical description. It would make scanning the text much easier during roleplay scenes.

A puzzle-game solution to social conflict could work for certain NPCs though, especially in cases where a lucky diplomacy die-roll might 'break' the adventure.

One of the reasons I like 'Naruto' is because combat is treated like a puzzle. You have to find an angle to win. You can't just overpower your opponent. You have to treat each encounter as unique and think outside the box about all the nifty ways you can apply your techniques.

I wish all conflict resolution was like this.