Knope I think that STEM subject degrees should be tuition fee free for everyone, and I don't think it should just be medicine or law, but I do think the expansion of higher ed has gone too far. It could be any bright kid who makes it into an RG uni, not necessarily those privately educated. Supportive parents come from across the social spectrum.
We have paid for ds's fees for his BA, and will be paying for his MA this year in full. We only have one child, and this is something we can do for him. Yes, that may give him an advantage, but I'd rather he got the benefit of our money now.
I also think there is a perception that because families have money, the kids have advantages, That isn't always true; and frankly, the attitudes of some of the better off parents towards their kids and their educations that i've seen have been poor.