Nope, capitalism is not doomed. There seems to be a cycle of capitalism to socialism and back, like a never-ending sine wave. When one becomes too extreme, we switch to the other. It's not a 100% switch, but it's enough to create a balance. It's a delicate balance, since going too far in either direction may result in a civil war.

Even in the utopian future that AI supporters are selling, a future where all our needs are met, people will find needs that can't be met by AI. So the cycle will continue as a way to allocate resources.