There is hardly any example of capitalism working without rather a lot of socialism - nor vice versa. Unless the primitive communism of pre-agricultural peoples count, in which case it's been the most sustained and stable system. Feudalism and, before it, slavery lasted a long time without capitalism. You couldn't actually be much wronger.
A combination of the two as practised in countries where left wing governments have been elected, pay enormous tax rates for their social security as compared to market economies.
Generous social security doesn't make you not a market economy. The more socialistic mixed economies typically have higher tax rates but hardly "enormous" for most folks, who enjoy the world's highest living standards.