I don't think it's clear to anyone this is true. We can see major wins even in the face of capitalist competition by countries with really quite socialist outlooks (a very good example here is Germany, who's modern government cribs notes from both "sides of the aisle" as it were).

But it's pretty clear that pure free market capitalism is going to face substantial challenges as automation begins on a massive scale. Every major economy is set up around the notion of "total employment" (everyone has a job that can pay for a basic liefestyle) as a precondition for their societal integrity. But as AI-based software systems begin to automate and improve manufacturing, transit and farming efficiency it will start to produce a massive decline in the demand for labor.

It may be as post-scarcity conditions begin to exist for labor, the definition of capitalism itself leans more towards social support structures. After all, a market economy without consumers finds itself contracting into feudalism; and that's not something many people without a few billion in assets are happy seeing.