Our current mixed system isn't balanced. When FDR introduced the New Deal, we had a more mixed economy, but lobbyists, free trade agreements, union busting, Glass Steagall, and diminishing the numerous Acts to protect the public and workers shifted our economy. The are many reasons why this happened, but essentially, our government transitioned the economic agenda 50 years ago or so, and wealth distribution decreased.
For capitalism to function for the working class, we need the government to regulate businesses and provide public goods. Otherwise, powerful monopolies control politics, markets, and society, and that's not democratic. When Obama and Bush bailed out the banks and not the homeowners, they demonstrated who the government works for.
Socialism and communism haven't failed, but after WWI, the revolutions in Russia, China, and Germany to overthrow capitalism didn't progress. There's a lot to learn from their mistakes, but peasants overthrew the wealthy elite, took power, and living standards improved. The whole event wasn't horrific.
Forever growth is a pillar of capitalism, and the economic structure needs population growth -hence immigration. No economic system is perfect, and in regards to population growth, which countries are you referring to? Perhaps to progress to socialism, population was necessary for production, but that's a component of capitalism. I'm not sure I understand your statement.
Lastly, capitalism has failed so many times it's hard to keep up, and governments just bailed it out again.