You also seem to think that somehow 20-30% of hospital beds being occupied solely by people sick with Covid is somehow not significant. Hospitals aren't designed to have so much capacity that they run on empty. Nor are they meant to be running at near max capacity at all times. But if a hospital is generally running on having 50-60% of beds occupied normally, and there is a surge like we've seen over the last 6 weeks that adds 20-30% on top of that solely because of Covid, then yes, its Covid that is causing hospitals to be overrun.
Come to think of it, two of those states aren't near the bottom, so that's also just wrong: Texas and Florida are around the halfway point when the states are ranked by vaccination rate, Texas just below and Florida just above. [0]
So yeah, I definitely think there's something else going on.
[0] https://usafacts.org/visualizations/covid-vaccine-tracker-st...
Arkansas: https://data.commercialappeal.com/covid-19-hospital-capacity... - Mostly not being overrun, and again covid is only like 20-30%.
Florida: https://data.commercialappeal.com/covid-19-hospital-capacity... - Similar to Alabama, and like Alabama, mostly not covid.
Georgia: https://data.commercialappeal.com/covid-19-hospital-capacity... - Only a handful are out of beds, with the covid patients looking like an even smaller proportion, around 15-20% in most of them.
Mississippi - https://data.commercialappeal.com/covid-19-hospital-capacity... - Only the smallest hospitals are out of beds, with covid again looking like the 20-30% range for most of them.
Texas - https://data.commercialappeal.com/covid-19-hospital-capacity... - About half of them are on the high end; Texas looks like it's in much better shape than the other five states. Again covid cases are on the low end, 15-20%.
If there's something overrunning these hospitals, it's still most likely deferred treatments from last year. (Edit: And as the comment sibling to yours points out, they're currently doing elective surgeries that can probably be postponed to open up more capacity if really needed)