Right now there is a serious issue with discharging patients from the hospital environment into skilled care. Since COVID, many nursing homes don't take admissions over the weekend, limit admissions to long term care (as opposed to transitional care which is short term - and better reimbursed), and often have wait times. This has the effect of increasing the length of time a patient is in the hospital unnecessarily, thus decreasing hospital capacity.
Yes, the nursing homes have staffing issues, but they pay for shit. Many of them pay less than $20/hour. You need to goto school to get your CNA license which isn't free. You can get many other jobs for better pay without the investment of education.
Source: I am a hospitalist physician. I work with nursing homes a great deal and my wife used to work at one as a CNA.