What if you DID cut out all social interaction skills? What if you just replaced it with another system instead of +roll?
Give players a pool of, I dunno... Influence and Resistance (marketing team working on a better pool name, TBD). From that pool of points, players can exert pressures of any social sort. Resistance is spent equally from the same pool, but here's the trick: Comparisons on spends are not revealed until both have decided, so it is a blind system.
Bob wants to intimidate the Detective, so after his amazing pose, he +spends 5 Influence points. This spend is NOT echoed to the room, just Bob. He has to give a reason and a 'target', Jane.
Jane the detective has a <Feat|Merit> that grants her +2 to resist any sort of Influence. But, reading Bob's pose, she realizes as a player what he is doing, and she decides to spend 5 points, because she knows that if Jane gets caught doing what he is demanding, she'll get prison time. So, with her +2, she has a 7.
The two players, having done their spends, get a reveal showing that Jane withstands the attempt. Now, Jane the detective proceeds to smirk at Bob and reach for her radio to call him in... <or whatever>.
This pool refills after a scene, every day, however works best.
EDIT: The key to the mechanic here is that the spend by Bob is silent. Jane only resists because her player cleverly reads the pose in question and realizes that he is likely doing some sort of Intimidation on her. If Jane's player missed that nuance, then she wouldn't resist... and only her +2 would apply and Bob catches her off-guard.
Of course, this would require a social contract on poses matching expenditures... but I think the community can sort that easily enough.