I don't think there is a perfect answer. Personally I want proficiency and ability scores to matter outside of combat. But I also want to balance it out and not reward just that.
So how I handle it is to have people explain what they're doing however they want. If it's a social situation, most of the time I want them to interact in first person, I enjoy it more. But if they're not comfortable with that, they can just tell me what argument they're trying to make. Either way I'll do my best to base the target DC (which will be adjusted and may go from automatic to virtually impossible) on the substance of what they say and anything else that may factor in such as interactions.
That is pretty much do with may be a bit less in character chatter as I am also not too hot at it but my current players do not seem very keen on it.
The problem with skill challenges as used was that there was none of that. The DCs were largely set in stone and nothing you said or did really mattered. Make a truly convincing case? At best you get two successes and someone else had to make further successes using a different skill.
If the decisions you make, if what your PCs say or do are meaningless and the only thing that matters is rolling a D20 and adding a modifier, it's roll playing. Now, maybe that's okay for some people. But in our games? Especially in LFR? Too often it was go around the table and the person with the highest modifier rolled. No creativity, no alternatives, just roll the dice and hope you get the requisite successes before exceeding the failure limit.
This is kind of what I felt about skill challenges, I think it should have been more a fail forward but with rising stakes type thing.
One thing I have found interesting is the study stuff in Strixhaven. It is a downtime for rerolls kind of thing. I could see it as a way to incorporate research/investigation in to the game better.
However, all that said, I am not sure D&D really needs a social conflict mechanic. Though I would be interested in any one that was developed. I think the mechanics we have are good enough but the DM advice could be better.
What I would like to see is a good journey mechanic. The current rules are a mess, the wilderness navigation DC table is arrant nonsense. A lot of the other are either too detailed or not detailed enough.
If people want to handwave encumbrance then the rules could be simplified to a well supplied group can travel x days, if they do not carry water and y days if they have to carry water, pack animals add +z days travel.
Foraging cost y time/x time travelled. Navigation is easy on well marked roads/trails, moderate on other terrain, hard on featureless (it all looks the same, dense forest/jungle) very hard on shifting terrain - wandering sand dunes, snow drifts. Modified by knowledge, time of year, weather, etc.
Hmmm.. I may be wondering off topic here.
I'm not saying there's a perfect solution. I keep a list of what people are proficient at and try to throw situations where they're useful now and then. Whether it's setting up a scenario where the fighter has to lift the portcullis using athletics while the warlock tries to distract the guard or the wizard tries to decipher the arcane writings on a map while the monk uses their cartography skills to determine a precise location. Sometimes I'll use a skill challenge structure. But if someone comes up with a really cool solution, probably something I didn't think of, they just succeed. Maybe with a role, maybe not.
So my preference is to leave it more open with options as described in The Role of the Dice in the DMG so groups can do what makes sense for them.
I do think more emphasis that these are ability check and allowing abilities to tread on the toes of the "skills" a little would be of the good.