If a hundred self-driving cars are available, then why would I care that you want to drive one north while I want to go south? If there are enough, it doesn't matter who get which one. Rivalrousness does not imply a need for market allocation. Are you really saying that we need property rights in a post-scarcity scenario because it would be impossible for a government computer to allocate who gets which box of super-abundant chicken wings? Yes, there would be a need for some form of use-rights, e.g. of your body parts, but not of actual property rights. Neither is there be any reason why this couldn't be organized by some authoritarian nationstate.
As for the incentive argument, magical assumed super-abundance solves that one too. Just imagine flying robots doing all the unpleasant work. Or assume away human nature and imagine people will work for fulfillment or the betterment of society. If you let the communists get away with assuming they can create superabundance, they will always win the argument. I understand why they would want to ignore the calculation problem, I don't understand why you would concede to that.