You're conflating market mechanisms as a general concept to the current global market. You can use market mechanisms as a resource allocation method in all kinds of different models. Market mechanisms are used in all kinds of settings to match prices of all kinds of things, and they work well when they are designed to be fit for purpose.
A market is ultimately nothing more than the iterative application of a function that takes a list of buy and sell orders and outputs matches. It can be entirely unregulated or however regulated you want. There can be no constraints on who accesses it, or lots. There can be synthetic manipulation on one or both sides to adjust the functioning of the market, or not.
I'd argue for all kinds of regulations - I don't think unregulated markets are a good thing at all. But a well regulated market is simply a consensus mechanism that reduces what is a fundamentally computationally intractable control problem if you try to handle it in a centralised manner by dividing it into a range of smaller problems and distribution the effort of figuring out the best way of meetings goals. It's never going to give an optimal outcome, but you can mitigate the risk that it will produce really bad outcomes, and get closer to decent results.
I'm also not arguing for one market, but for many, I favour using market mechanisms to price externalities whenever possible.
The current global market is not set up to "properly distributing resources" because that is not the goal of its participants, so you have a good argument against current global markets for products. If you were to create a market actually intended to fairly distribute scarce healthcare supplies and it would look very different, with pricing based on e.g. predicted outcomes and benefits for different bidders.
You can still plan in the face of well regulated markets, but the planning process would involve packaging up incentives and regulating the pricing of externalities without trying to guess what will work best in ways that forces the planners to become experts in everything.
> The lack of control you seem to present as an advantage is exactly what makes it controllable by a very small minority of powerful entities.
Even if we were to agree this was unavoidable (I'd agree it's unavoidable in an unregulated market with vastly different access to resources, but that is just one subset of possible markets), a planned system is potentially controlled by an even smaller entity of even more powerful entities. We've seen that fail time and time again, because of the hubris of people with power thinking they knew best. Decentralising power is if nothing else a risk mitigation, and the failure of current markets to do so well enough is not an argument for a mechanism with a distinctly worse track record.