Total, complete naive guesses from an amateur who has no idea how hospitals work:
Can it be a attributed to a scenario where hospitals need minimum occupancy for various wings to account for higher variability in lower populations? South Dakota has a low population density, so their spikes and lulls in hospital need are going to vary much more drastically than large populations. (you are more likely to see a 20% swing in pregnancy rates in a low population than a high one due to mean regression) So those states are more likely going to need to prepare for those swings. Especially if a hospital is segmented, so they need enough ICU beds and maternity beds and long term care beds to handle all of this. If you had a population of 5 people, just from sheer luck you could have 60% of them in the hospital at once. If you have a population of 500K people, this is less likely.
Now maybe combine that with poor populations being less healthy in general, and those states are looking at higher variability and less healthy populace.
Those are just guesses. I wouldn't say they hold much weight, but stats can be deceiving.