I remember when I was 35 and suggested the bolded above to my 65 year old Mom. She just about blew a gasket. She paid into it and she was intending to get the promised benefit from it. Now that I am approaching 50, I'm coming around to her way of thinking, funnily enough.
Anyway, by means testing you are just punishing middle class and upper middle class savers. The rich won't care if they don't get their SS checks. But those middle class and upper middle class savers (you know - the salt of the earth - the people who played by all the rules) tend also to be retirement planners as well as savers. Pensions are mostly gone now, but SS remains as a COLAed "pension" that a person can plan around. You just screwed up their plans, and reneged on a multi-decade deal they had been going along with.
So I guess if your means test doesn't bite until say $10M of net worth, I'm OK with that. No less. Go bother the rich (hint: capital gains tax increase) or adjust the SS retirement ages. Leave the middle class alone for once.