I quite like this and use a variation of it as well in my games - letting players substitute relevant skills as social skills where it makes sense makes me happy. Though the way that I do it is that it isn't the skill, it's just if they have a relevant skill or proficiency then I let them add the proficiency bonus for that skill to their Charisma or Wisdom checks (so expertise counts, but they don't get to use their full Acrobatics bonus to get onto the circus acrobat's good side). If they have a tool proficiency that's relevant it's the same - so the guy trying to get onto the gambler's good side can use his card proficiency bonus on his Charisma check even if he doesn't have a relevant skill for it. It's basically in the same mechanical ballpark as other game systems where you can mix your skill and stat bonuses instead of having a skill depend entirely on a single stat.A simple thing that I've used a bunch is to make most of the skills also social skills in terms of getting along with and interacting with NPCs who share a skill set. So someone with Animal Handling can do social stuff with drovers and drivers. That sort of thing. I find this opens up a lot of character builds to actual usefulness in social encounters without actually changing the mechanics of the game at all. It also makes sense in a 'shop talk' kind of way.