"a young lady who had just finished her expensive education at one of Edinburgh's more expensive private schools. She was very confident, but utterly ill-informed about matters of fact."
I've encountered people like this on numerous occasions so I find this utterly unsurprising. Thankfully not all privately educated people are like this, but a significant minority seem to be. One of the side effects of privilege is not terribly bright people who ooze confidence and a sense of entitlement. Not what you know but who you know, and all that.
She was probably a Tory so you were onto a loser there anyway.
"One of the things I hate about the present system is its overpromotion of polished, plausible incompetents due to their connections, self confidence and money. We lose out on so many intelligent and energetic people who are born in the wrong houses to ever get near power."
I'm not convinced independence would change that. Elites look after their own, whether in a smaller independent nation or not. One key difference in an indy Scotland would be the high road to state power in London would be firmly closed to ambitious types. Instead, they'll end up as EU functionaries or something to do with the UN. Arguably a better state of affairs if they are representing the country of their birth rather than lording it over us as a representative of the British state.
One thing that would erode privilege and all its ugly manifestations in Scotland is land reform. This is not dependent on independence, the Scottish Parly has the powers to do most of what is required if it so wishes. Indeed, a recent SP report on land reform has fair put the wind up powerful landowning interests. You can safely bet that, in the event of a No vote, those interests will be lobbying Westminster very hard to remove certain powers from Holyrood in order to protect the status quo regarding land ownership.