Intimidation. Why is this a single number? When you actually try to intimidate someone their reaction to that depends on (a) their sanity (b) their perception of your combat abilities (c) their perception of whether you will actually follow up on your threat (c) their perception of their ability to escape (d) whether they want to help you or not regardless of your nasty behavior toward them (e) whether there are outside factors preventing them from helping you, despite your attempt at threatening them (f) so on and so forth. Only (b) is a factor that doesn't change depending on who you're talking to. How can this be governed by a single number on your stat sheet?
Nobody argues that real life is a lot more complex than the most detailed character sheet and that a single number defining your ability in any given field, be it sword-fighting, science, or intimidation, can't approach the real life's complexity. It's done for convenience. However, just because having two sets of numbers (your skills vs the NPC's difficulty level, which encompasses a, b, c, d, e, and f) isn't sufficiently complex doesn't mean that it should be eliminated entirely. It's a case where something is way better than nothing.
Diplomacy/Persuasion. Why is this a single number? Similar to Intimidation, maybe even more so, diplomacy is all about context. Sure, some people are better at diplomacy in general. And this is more of an internal character trait than being based on how scary they look. However, countries are constantly interacting with each other through diplomacy. And, in the end, a country is going to do what it wants to do. People are similar. Diplomacy is about convincing somebody that a course of action is in their best interest when they initially aren't convinced. How can this NOT be a contextual action? Your character would need to be privy to all kinds of information beforehand in order to solve a tough diplomacy problem. Simply having a sufficiently high single number on your character sheet doesn't cut it.
First, throughout history, some diplomats, even in the same countries (like post-revolution France) were considerably better than others. Talleyrand is a good example. Much disliked by everyone for his legendary amorality, he served five different regimes (which wasn't easy being both a noble-born and a priest - not the most popular backgrounds in France at that time) and every attempt to replace him with lesser people who were, of course, "privy to all kinds of information beforehand", ended in failure or poor results.
Second, diplomacy is a bad name for the skill. Persuasion is a much better one. As you probably know, I worked in sales for a while and know the industry well. I can assure you that you can line up tell well-spoken, pleasant and sufficiently charismatic people of similar intelligence, train them for a week, send them into the world, and observe vastly different results. I've seen people who simply had an uncanny ability to talk people into buying shit from them (i.e. establishing instant trust, overcoming their fear of making a bad decision, convincing them that they need whatever it is they were selling, weakening their positions on the issue and making them doubt it, etc) and they did it in a very effortless way. I've seen people who couldn't sell if their lives depended on it, despite being trained, being social and outgoing, being good talkers, etc.
So, again, it's more than a single ability, it's 3-4 abilities working together, but in an RPG a single skill will suffice.
I could go on but you get the point. Social interaction is intellectually contextual and therefore extremely difficult to scale across a large number of encounters.
Having a single skill and different difficulty levels representing various abilities (one NPC can be hard to convince because he's knowledgeable and his positions are well defined; the other can simply be distrustful of everyone - the outcome in both cases is the same, the PC needs to be very skilled to overcome the arguments in one case, the distrust in another). Additionally, one can do what we did in AoD: add supportive skills/stats - INT/lore in the first case, charisma in the second.
Also, the context is easy to replicate by tying lines to what you did, what you learned, specific conversations, etc.