I don't know how they decide to do that. I got one after my 3rd visit to the ER needing a treatment. You might ask about it.

When I had double pneumonia, plus pleurisy ,the er Dr prescribed the nebulizer and the meds to be used with it.
Don't know why there is such a problem about getting the Dr to prescribe one ,as I had asked previous Dr for it.

I think I'd ask them why they won't prescribe a nebulizer.

I just went to the drugstore and bought a machine and my Dr gave me prescriptions for the capsules of nebulous

I asked for mine.