There is a real possibility of this. Here is WA state hospitals are overrun with patients from Idaho. Idaho hospitals are full and they are rationing care to those they believe most likely to survive (regardless of vaxxed state). That means the really sick and those of advanced age or underlying conditions go to the back of the line.
In WA, even though hospitals are not yet 'officially' taking this same tack, it is in fact going on. Beds are full, local health authorities are pleading with people not to do anything that might results in an accident (like gutter cleaning) and routine care and surgeries are being cancelled for lack of resources. 2 weeks ago I had an annual exam at a nearby medical center cancelled for this reason.
In my rural area patients who go to ERs with a serious cardiac issue or major trauma are routinely transported to Seattle, Tacoma or other larger centers. For the past 3 weeks or so these facilities have been on bypass - not accepting these emergency cases. The overload is real and people are dying, waiting for care.
When boosters are available I'll be in line.