that social democracy makes people rich, and capitalism makes people poor.
I don’t think you have that right. In either system a smart person can become rich. Only under capitalism can you get rich by hard work. Under social democracy you still have capitalism, thankfully. When you say capitalism you really mean Oligarchy. You can have Oligarchy under social democracy and the social commons provided by that Oligarchy might be penurious.
You see the state can only provide benefits commensurate with the productivity of the culture. Without capital investment a state would be much like Afghanistan.
It is the allocation of the proceeds of capital investment and the productivity of the efforts and assets of a culture that determine its prosperity. Because the Oligarchs seem to demand to keep most of the proceeds for themselves we have penurious social commons. With high productivity and high capital investment we can afford a generous social commons but the electorate doesn’t demand a generous social commons because the working poor and lower middle class can’t stand to see the poor, disabled, disadvantaged and others not suffer for their inability. Even in a social democracy that attitude would still affect policy. It would still be a democracy and their votes would still count.