So you claim to be an academic high achiever, but have never met any of these bright but disorganised people in real life?
If you did, you'd explicitly state the fiction reflects the reality based on your experience.
Instead, you have assumed that things popularised in fiction are true... which, erm, isn't very intelligent. Not only that, it's also a damaging assumption, particularly in my STEM field, when people make assumptions because of perceived stereotypes, as you are doing. Perhaps I've misunderstood your point.
PA's having a degree isn't a big deal, in fact it's very common these days as there are too many people with degrees and not enough jobs.
But to answer your question, Oxbridge students are required to excel and be academically curious in their own field of study. If it's STEM, why would you expect them to know about 'lots of things'? Furthermore, they may also be presenting a 'professional' self at work.
I'm one of the types you're thinking about. I have a wide range of interests, my brain works in weird ways, I can make connections between things others don't. I'm also scatty and disorganised 😎
However, I don't present myself like this at work. Or at least, not the vast majority of people I interact with. I moderate my behaviour and communication style depending on my audience. As a female software engineer it's doubly important because me talking fast makes people think I'm nervous, junior and incapable even though what I'm saying makes sense. Also, no matter how intelligent you are, there's a time and place for deeper intellectual conversations which may not be the workplace where opinions on politics, finance etc can be very divisive.
You'd need to know these people very well before making deeper judgements.
FWIW, I went to LSE and was surprised to see that quite a lot of people were 'normal intelligent' however this was in the STEM courses, which didn't have much required discussion. The humanities students wouldn't have gotten away with that as there were weekly discussion seminars.
In Oxbridge even STEM courses have a lot of individual discussion with academics so it would be hard for someone to get away with it?
I work with a lot of Oxbridge students, half my best mates went there (undergrads, postgrads, PhDs). The intelligent types you talk about however come from many places.