Here's my hot take: no mechanical system can make an encounter interesting. It doesn't matter if it's crafting, combat, space/vehicle combat, or a social encounter, the principle is the same.

For an encounter to be interesting, you need all players to have independent agency and involvement, multiple viable strategies, multiple things to engage with in different ways. The reason why, for instance, space combat is hard to make fun is because, even if you give every player a role on the starship and a complex system of energy management, if it's just two ships in a duel in empty space, there's not a great deal of viable independent agency for players - you basically cooperate following a fairly rigid script.

But, taking the space combat example again, if there is "terrain" in space - zones with hazards, "warped" zones - multiple objectives and opponents, and multiple ways to deal with them - civilian ships to protect, borders to repel, fighters to engage, cyberattacks to launch - then you naturally get interesting things happen, whatever the mechanics are.

This doesn't mean you have to make every encounter complex - but if the encounter isn't complex enough in itself to naturally lead to an interesting scene, then I'd just storm through it with one or two quick rolls. You can do something more extended with multiple rolls, as long as they're resolved quickly.

I think the same thing applies to social encounters, and that's why everyone struggles to find a really good system for them. If you have a multi-stage criminal trial, then there's a lot of room for creativity and a lot of moving parts, so immediately you can run it and make it interesting with almost any mechanics you feel like. But if you're trying to find a mechanic to turn a simple attempt at persuasion into something more complex, I think it's best just to keep that as fiction-based judgement plus one or two rolls, if any are needed at all.