Capitalism is a method for distributing scarce resources. Remove the scarcity and you remove the need for capitalism.
Nor are all alternatives to capitalism socialism. Socialism is also known to have very severe problems in application, particularly how to incentivize socialist managers to behave like capitalist ones in most circumstances, driving innovation and maximizing productivity. Socialist managers have somewhat different contstraints on them from capitalist managers, and nominally different long-term goals, but they are more similar than you might think.
The thing is: we know how to make capitalism work in a range of varieties, from the Scandanavian social democracies to the mess that's Texas. We have never seen a successful system of public ownership of the means of production (which is what socialism is, and nothing else). It has been tried in a variety of places and times, and it has always run up against fundamental problems of managerial incentives and political corruption at levels that make most capitalist political economies look pretty good (which is saying something!)
So looking for non-socialist means of distributing wealth in a society that is unequally post-scarce is a good idea. Today wealth is distributed almost exclusively through paid work, but that is a relatively recent invention. I'm not suggesting a return to feudalism or anything like it, but think we should be willing to consider variations in social order that are at least that large-scale, because the difference between what is coming and industrial capitalism is going to be at least as big as the difference between industrial capitalism and the semi-feudal societies that preceded it in many places.
The majority of production in Sweden is not state owned.
Actually, socialism is the ownership by the workers of the means of production.
A system of co-operatives would also be socialist.
If post-scarcity is brought about by automation, then there will be no need for most people to work, and socialism won't be the appropriate economic model (since people will not be directly involved in production). At this point we'll probably need to return to a gift-like economy.
Free markets and trade have lifted the most people out of poverty and improved the living standards of the largest number of people in history.
It is an imperfect way of organising the needs of people, but it is superior to everything else that has been tried, by an order of magnitude.
This is extremely important to remember. The fear of the unknown should not stop us from trying new economic systems that may be superior to capitalism.