As an asthmatic, who cannot lie flat at all during a bad flare, it’s very counterintuitive - but in this case I’d have to assume the doctors know what they’re doing. There are even special beds that rotate 360 degrees along the long axis, though they aren’t common.
Other treatments that have increasing evidence of efficacy:
Dexamethasone (a somewhat longer-acting corticosteroid, versus prednisone which is my Very Good Friend when I have an asthma flare) - I believe Trump had this
As a lesser alternative to a ventilator, some hospitals have tried using CPAP machines (used mostly by people with sleep apnea) with mixed results. It can be helpful for patients with short hospital stays, but makes things worse for patients with longer hospitalizations, and because they typically release the patient’s exhalations into the room, the air blowing out of the mask’s vent carries virus particles which can infect others. (Two links below.)
I would add that the mask itself has to be integral to the filter. My CPAP mask is designed to leak at the junction of the hose connection. So adding a filter requires a tight sealing mask that vents back through a filter.
Like any system in place, it can’t just be thrown in a box and stored for emergencies. These things have a life span so they would have to be either easily scalable or a stockpile that is rotated or replaced periodically.