Anyone, no matter how wealthy or otherwise their background, has a right to apply and compete for a university place if they have the necessary intellectual capacity and evidence of that.
However, they (and their parents) shouldn't feel pressured into going just for the sake of a 'good education', which is what I could see happening if it became 'the norm'. A university education should remain something that people have to work hard for and work hard at, not something to which everyone has an automatic right. Otherwise there'd be no value in it.
I come from a very working-class background - my parents were both factory workers - and didn't have any ambitions towards uni when I was younger, even though I'd had a grammar school education. I didn't actually go until I was 36, when Ifelt ready. My own kids knew I would support them if they wanted to go, but in the end neither of them did. They both seem to have made a fair success of their lives despite that.