There is a cap but I think a large part of that is to prevent people from complaining about the size of pensions paid out by the government. What you get back from the program is a function of what you put in and if you allowed people to put in the portion from $1 Million of income you might owe them $200K pensions after 40 years. I don't think the public has appetite for that.

I don't have to pay more for my house insurance if I make more money either.

So what?

But the output is depending on how much you put it, it’s actually progressive. Just less so than taxation in general.

Yes, it's progressive if you just consider the lower and middle class. Actually I think if you get what you put into it, it's neither progressive or regressive. If you include the upper earners, it's regressive. It's as if they capped income tax to your first $100K. Great for one group of people, not for the majority other.

You get more benefits from the first dollars put into SS than the last as far as I understand.