I do agree that the existing economic system, whatever it might be called, has a dearth of competition. I'm not sure that "restoring" competition is possible or that it would solve the societal problems of unemployment, poverty, and sustainability.

I prefer to get the political component out of the definition of capitalism. It is best defined, I think, as mass production of goods and services for sales in geographically extended markets.

As for changing the outcomes for society of any nation's existing economy, another possible approach would be to change the way money (as currency) is supplied for the economy. Make it an income paid to eligible citizens. Unemployment and poverty would be eliminated (at no cost to anyone, without having to redistribute anything) while sustainability would be increased. Even better, taxes/public debt could be eliminated and the economy become fully self-regulating.

"For Crying Out Loud, Accept That A Solution Actually Exists" (a "3 min read" — including options for further reading — here in Medium)