It's a subtle difference, but I think it's important. We've been told from movies and books that heroes are never intimidated. So, being intimidated seems like a weak and unheroic trait. That by controlling their fear, that's what makes them heroes.
And that, to me, is a key difference is the types of stories that movies or novels tell and the types of stories that can be told in an RPG. Over the course a of a campaign, player will see the weaknesses of their characters and will have to deal with them. A veteran orc fighter can still be scared by an orc; it's not easy, and I would certainly give such a character a mechanical boost to avoid it, but it can still happen. The key to me is what happens next. You mostly see the next part in movies and novels, but there still has to be those moments, whether they are shown or not, that triggered the next part. Heroes didn't learn to control fear because they just can; they did so because they have practice in experiencing it and dealing with it. A movie rarely shows those moments of weakness that serve as the reason that they can control it later. A tabletop campaign shows every notable moment from starting level to the end of the campaign, and not all of those moments are going to be superheroic; there will be a lot of stumbling that occurs before the superheroic stuff occurs.
On intimidation, the key in my minde is that the successful check instills fear, but fear is a very tough emotion to use to guide someone. Even the fear spell, which dictates that the usual response is to run away, makes it clear that someone who can't easily do the standard response is still perfectly able to choose other options. The goal of the intimidator may be to get a specific reaction, but of all the emotions, fear is definitely one of the more unpredictable. Trying to pin someone down into a corner, whether it be a real, physical one or a mental one, is an uncertain exercise even for the most trained intimidator in the world who can eliminate the large majority of options available to their target. A roll can very much be used to force some kind of reaction, but the roll by itself does very little to control the precise nature of the reaction; better rolls get sharper reactions, but also more unpredictable reactions, so control remains elusive.
The other social skills are in a similar boat. I may tell someone that their PC fully believe someone who is lying to their face if they completely fail their check to see through the bluff. But all it takes is for someone else in the scene to put that little ounce of doubt back in the PC's mind for that failed roll to have noticeably less impact. Similar things with diplomacy; the roll can get a very real effect, but other aspects of the scene can very easily dampen or strengthen that effect.
And the last key part in my campaigns at least is that few social rolls are ever made in true isolation. They are almost always made as part of a larger scene. The roll very much effects that one aspect of the scene, but just like one player's RP can potentially override another player's RP, so too can the actions of another character minimize or strengthen any particular dice roll. Since there is almost always another PC around to support the affected PC and give them reasons to respond to the attempt different than how the one who initiated the response expects, the dice roll, in resolving one particular action, sets up an opportunity for the party to work together to shape the response. There will be times where the dice roll does basically determine the outcome, but those moments are rare if the party is working together to actively avoid them, and more notable because of it. I would get bored as a player or DM where such moments were common, but as a relatively rare thing, it can help make a scene stand out and make it that much more memorable.