You select the level of abstraction for different things based on what is and isn't the most fun to delve into. If your group enjoys poking every surface with a 10 foot pole, it's not wrong to play with that level of granularity. It's just that all the interesting things you can do with a 10 foot pole are pretty mined-out after 50 years so we tend to direct our attention elsewhere.
Yeah... It's important for the group to be on the same page about what's fun.
Me, I don't really want to do a blow by blow conversation with every NPC. I just want to say "I dazzle him with my brilliant smile and wit, and after some small talk try to learn about what's going on with the royal stable". I emphatically do not want to roleplay that small talk.
I wonder if there's an RPG out there that has complicated and precise rules for diplomacy, but then once combat starts you just make one roll to see who wins.
I'm not sure it scratches the itch for you, but you can play Shogun: Total War this way. You can manually direct your army in battles if you want to, but it makes the game take waaay longer (and I usually do poorly). Or you just auto-calculate the results of the battle and you get back to farming resources and taking over your neighbor's territory.
One idea I had for diplomacy is to have a triangular battlemap where the corners represent logos, ethos, and pathos, but I'm not really sure what to do beyond that. Should there be some kind of elemental rock paper scissors going on? Or people are just weak to certain types of arguments? As much as I like the idea of making a complicated system for arguments, I'm sure someone else has done it better and I don't know how to find it.
There is Dungeons and Discourse, based on this and this comic. One version here and another here.
First part hard yes, but that's actually explicit in OD&D. The slow adventuring pace in the dungeon accounts for probing etc.
Last part hard no, you just need to get more creative with obstacles. Like "traps" don't have to be hidden pitfalls. They can be wizardly match stick puzzles of doom and so can a 10 foot pole be incorporated into the puzzle by delicate magical manipulation by a magic user giving you a free move?
I'm not very creative, I just steal from media I like, but the sky is the limit when you stop playing character sheets and start playing the characters that the sheets abstract the wrote bits of.