If you want to make the argument that anything that is essential should be publicly owned you can make that argument. But I would suggest if you want to make that argument 'nobody should make profit' shouldn't be the relevant argument. The argument should be 'this is how we can solve X problem efficiently'.
Universal healthcare solves the problem. The US is #1 in science and tech, but spends the most with worse outcomes in general healthcare than other peer countries by far.
Okay: it’s obviously inefficient for some people to collect profit on essential services where competition is meaningless. That money should be going to improving the service for all, or paying the workers better, or ideally both. It would be more efficient to collectively organise food, shelter, healthcare, and other natural monopolies. Market competition can be for non-essentials where some inefficiency is acceptable.