The businesses are hardly profitable. For every dollar they get from housing a resident, they get just above half a penny of profit.
As I showed above, you can take the entire profit and put it into hiring more staff and it won't actually make a difference. They either need to raise prices, cut costs elsewhere (maybe administration? I'm not familiar enough to know), or pay people less.
That's what the numbers say.
Again, it doesn't matter whether you find the argument about compelling.
If care cannot be provided profitably, it won't be provided at all. That is reality. Somehow, the care must be paid for.
Those who need care are not better off if these facilities close.