I'm still not sure you know what capitalism means. Social welfare programs are not a form capitalism. Capitalism involves private owners and profit seeking. Capitalism in this context would be a corporation having a program that feeds hungry children and turns a profit off of the tax breaks and free marketing. A for-profit education system would be an example of capitalism. Social democracies have government-based safety nets that provide everyone with the essentials to have basic opportunity. The idea that capitalism and socialism take place simultaneously in a country still alludes you.
No you didn't say it, you described it then claimed it was equality of opportunity. If social welfare programs are not based on Capitalism, how are they paid for? So you just wave your magic sickle over a pile of sand and make a bag of groceries? If the corporation is feeding children, what the fuck is the problem? Isn't that what you claim you want? You keep telling me about how you don't advocate for collectivization and state control, but here you are literally complaining about kids being fed at the expense of state control. "Government based" is meaningless. The government doesn't produce anything, the government can only provide what it has taken from the productive by force or coercion. Your "social democracies" pay for these exceptionally smaller scale entitlement programs with a combination of extremely high taxes and natural resources sold on the world market, both dependent on what is known as Capitalism.
You aren't revealing some secret to me. I know they both can exist at the same time. The problem is you don't have any concept of the fact that Communism (Socialism) requires Capitalism to operate, but Capitalism does not require either Communism or Socialism to operate. Additionally there comes a point where entitlement programs become destructive of the very mechanisms which fund them. You however seem to think we can just keep handing out more and more and more, and because you feel on an emotional level that it is moral, some how magically it will work.