One issue: I'm seeing an effect of succeed/fail design here.
Certainly. Thats a further step that could be taken is to implement a Degree system. You could do either one to help the issue but I think the ideal is both.
Does the build have to be respected, though? Why even have a social "build" if the good role-play must be respected? Conversely, must a player's physical ineptitude be considered when he rolls a critical hit in battle?
If you're giving it as an option, not respecting it is going to cause issues. (See 5e and the myriad things it promises and fails to deliver on)
And its also important because not everyone can or is always going to want to engage in in-character improv. While this idea wouldn't make not doing so strictly "optimal", it wouldn't be punishing either.
And no, because most players aren't going to get up and start sparring to resolve a fight. Many, if not most, will readily speak in-character, and especially nowadays thats part of the appeal of these games.
Ultimately, this seems to be increasing the GM's workload.
It would lessen it, unless we're going to act like having to make a die roll is a significant increase in workload.
Its a lot easier to say a given bit of roleplay deserves a particular bonus than it is to sit and judge of an NPC is going to be receptive to any given argument and then pick out an appropriate DC that'll thread the needle on making the player feel good no matter which way the dice goes.
Instead, the player sets most of the DC, if they roleplay well they'll get a relatively small bonus to that DC, and the GM simply rolls the save and responds accordingly. Ezpz
If one recognizes how they argued should have had a high chance of convincing the person, and they fail the roll, that feels incredibly arbitrary because the player's roll has no tangible connection to the roleplay.
An NPC reacting to an argument, however, doesn't
have to be connected to the roleplay mechanically to feel right.
Frankly, Id go as far as to say this idea works better even if you assume zero in-character speaking and its all just mechanics.