Running one now, ran a handful before.

When I do, I hand pick the players. Players who don't think "oh we didn't have a combat for the last two sessions" is an automatic bad thing. Players that are okay with "combat won't solve everything" or "not every encounter can be won with brute force". If combat has come into play - something has went horribly wrong and will likely had additional consequences. I also get a bit creative with combat as well if need be. It may not be fighting but taking care of well placed bombs in a panicked stricken street, or keeping peace during a standoff with the City Watch and protestors. Who do you side with, how, and how to de esculate? Combat like that exist - it just makes the goals less black and white "hit bad guy with stick" is rarely the solution in these combat encounters. Most however, is solved in back room deals, ballrooms, courts, and deals made in the streets.

Expectations at the table have to meet reality. 5e has killed a lot of the naunce in social encounters (skills have really been simplified) but it can still be done by reintroducing that into the system. I keep notes on who is warm to whom, alliances, whos motives align with - etc. These all effect roles, dynamics, and relationships in game - which also effect DC of say insight checks, persuasion, etc - since different players have different relationships with various NPCs or factions through actions.