This latter camp might have diverse opinions on how much aristocracy they’d prefer, but that’s a distinction of degree not kind.

I think degrees matter critically, and that it isn't reasonable to lump all these people into 'one camp'. We have a instinctual behavior to provide for our offspring, and to compete on their behalf. IMO, it will be nearly impossible to prevent the transfer of wealth, and at some point, the energy spent doing so would cost more than the social gains. There's a big ideological difference between someone who would put caps on transferred wealth, and one that wouldn't. I strongly believe that the hereditary transfer of wealth should be limited, yet exist, but that doesn't mean that I'm concerned with preserving inequality, so much that it means that I don't want to create a system of governance that runs counter to human nature to such a degree that more harm than good is done.