There are loads of other economic systems. Feudalism, oligarchy, tribal pastoralism, you name it.
I was mainly thinking in terms of critiquing the idea that value is created by labour, since HyperSane mentioned it twice in comments.
It happens that the labour theory of value in central to Marx but it’s not exclusive to him. Adam Smith indulged a lesser form of it in one of his uncharacteristic slip ups in economic theory. However it is in Marx that it achieves its most vertiginous heights of absurdity, and through his disciples that the most damage was done by it.
There is a direct causal line from the LTV and some of the direst economic disasters in human history. The most egregious case, despite some strong rival examples in Soviet Russia, is probably Mao’s Great Leap Forward which among other things fetishised steel production. Production creates value and steel is the most important economic product, so everybody should make steel.
It’s the damage the LTV caused itself that I was talking about. Communism is a political project associated with it but not directly what I had in mind.
As for innovation, I’m all for it. Capitalism maximises individual freedom by putting ownership of capital and rights of self determination of labour directly into the hands of citizens. By maximising individual economic freedom it maximises opportunities for economic innovation. This is why free market capitalist economies are so creative and dynamic.