It helps when a group agrees on the kind of game that D&D is good at supporting and then works toward that goal together.
I agree with that. When we're doing the sort of non-adventuring I was talking about...we're barely using the system at all. Not even ability checks for most of it. The party plays with cantrips and I look at their passive "knowledge" skills to determine what information they get for free, and their Charisma and appearance to determine how people initially react to them. But other than that, it's more freeform role-playing than anything else at that point.
I'm a strong proponent of using the right system for the game and setting you want to play. Not really a major topic for the D&D threads, but it's a hugely important consideration for an RPGer overall.
In this particular case, I'm actually not a fan of systems having rules for this sort of freeform role-playing. I've tried to like them and failed. Rules are for when you need to consistently determine things that go beyond describing environments and role-playing the choices and conversations of PCs and NPCs. (In the rare instance during such role-playing when the results of an interaction attempt with an NPC are non-obvious, the DMG interaction rules are actually pretty decent. Much better than the traditional Charisma check irrationally opposed by their Wisdom rather than their resistance to the idea.)
So, for my tastes in what I want rules to cover, I'm not sure D&D is any less suited for this particular element of play than most other games. Of course, if we weren't spending enough time doing the sorts of things that D&D is designed for (mostly combat with some exploration) there wouldn't be much point using D&D for the game at all.*
*Well, I guess in this specific case there would be, since I don't like playing D&D settings with other rules systems, but that's a peculiar idiosyncrasy in my relationship to D&D and its settings, not a general RPG philosophy.