Lumifer is a bit heavy-handed with his name-calling, but I think his objection is basically the right one.

The market is an information processing machine that solves problems too complex to be solved by any other means we have yet tried. Our entire experience with non-money economies is a stupefying lack of efficiency. But the OP asks about getting rid of ownership, not money, and that hasn't been tried.

So I have a refrigerator with some food in it and I'm set for the next day or two eating-wise. If I don't own the food in the refrigerator, by any reasonable definition of ownership I can think of this means I am NOT set for then next day or two as anybody who can reasonably predict that at least a few people have food in refrigerators can believe that THEY are set for at least the next few hours because they can walk up to those refrigerators and take the food. Without ownership how is that avoided? And don't tell me by "politeness" or "convention," the politeness and convention you would be appealing to is that you don't take other people's stuff, i.e., you have let ownership seep back in to your system.

And beyond the food, I don't even own the refrigerator! And the good folks at the power company may conspire to make 99.99% reliable electricity for the refrigerator, but currently they do that because it pays well, so in this other system, do we have a mechanism to suggest that this will still happen?

Considering the difference in productivity between market economies and non-market economies, empirically you'd have to estimate that the market system is about as important to production as are lungs to the metabolism of land based mammals. Sure, without lungs, there'd be some way of getting some oxygen to the cells, but probably 1e-3 o 1e-6 as much or some such crazy reduction.

If you want to get rid of money, but you don't want mass starvation, pollution, diseases, dehydration, and all the other things that would occur with a cratering of production and distribution, you need to propose a system that will take its place. It is not the job of people "accepting your counterfactual" to assume that there is a reasonable one in the wings. And if people don't argue against your counterfactual proposal to replace money, they are probably just uneducated in economics.

About the only counterfactual I can guess is that humans get taken care of by a different intelligence. Whether that is machine AI, or Aliens, or cyborg slave chimpanzees and apes, I would bet dollars to donuts that our caretakers providing us with all the stuff we currently get and then some, will have something which is informationally equivalent to money in their system. No matter how smart you are, there are just a whole class of decisions which when distributed cause a system to be more efficient than when those decisions are centralized.