You’re starting from a false premise, Op.
I don’t believe that most people do want to eradicate the rich. Communism is not popular here.
Nor do I believe in “the politics of envy”. That’s just a silly phrase dreamed up by people with a great deal of wealth who want to keep it that way.
What I do think is much more popular is the socialist model that you’ve taken great care to avoid, though several posters have laid out what they believe.
Most people are indifferent to others’ wealth so long as they themselves are comfortable. They don’t envy the rich, they simply want themselves and their families to afford to eat decently and access good schools, housing and healthcare.
That’s perfectly achievable without doing away with rich people or taxing them into oblivion.
What does anger people is the super-rich sitting on their billions when others are living in poverty.
The trickle-down philanthropists don’t work - and why should their priorities be indulged when they are unelected? Why should we have to beg for funds from someone playing God Almighty, and enjoying the power it gives them?
The rich might pay more tax, but proportionally they do not. A poor person, with less, or even no disposable income pays a far greater proportion of their income on tax.
Stop quoting stereotypes about the politics of envy and consider the reality: the ordinary people who work long hard hours, yet struggle to put food on the table, or worry about heating their homes, or the next unexpected bill that they cannot afford.
You’re blaming them for their poverty - the undeserving poor who made bad life choices. That’s another stereotype the wealthy love to use to ease their consciences.