Why are they scarce?
Address the scarcity and you don’t have to allocate.
Look at this like a Chicago Democrat, and the answer will be obvious.
When you have a bureaucrat deciding who shall live and who shall die, imagine the "considerations" for getting to the front of the line. Who would dare to criticize the Powers that Be, if that might mean that their family might not have a "priority" for needed medical care?
When you have a market solution, increased needs result in higher prices paid to providers, which result in increased capacity (more people going into medicine, people working overtime, people coming back from retirement).
In a bureaucrat system, the political class has an incentive to drive DOWN capacity, since that will increase bribes from people needing to get to the front of the line.