Beyond the roleplaying at the table issue, I find Diplomacy is too broad, and bluff/intimidate are too narrow.
Yeah, you have a point there.
I've seen countless skill challenges in adventure modules now, and there's only a very small minority where it's ever useful to use intimidate.
In contrast Diplomacy almost always grants you a success. Bluff's somewhere inbetween.
I believe part of the reason may be that Intimidate is seen by the developers as an in-combat option rather than a diplomatic tool.
Anyway, it's one of the reasons I prefer ad-hoc skill challenges: All skills can be equally useful if the players' roleplaying and/or argumentation is convincing.
Imho, while players may complain if they did great roleplaying but failed their skill check because their character simply isn't as eloquent as the player is, they'll just have to suck it up - or create a character that is actually good at this stuff.
If a rpg system has a skill system to decide on the success of diplomatic endeavours than it should be used. A player who makes an investment here, has to be rewarded. Otherwise you'll end up with a situation I've often seen in previous editions:
Everyone uses Charisma as a dump stat but it doesn't have a negative effect ever, because the player's such a charming person.
I.e. the alternative is to get rid of social skills.