I have found that most of the assisted living units in my area, Columbus, OH,will only accept medicaid waivers for private pay residence. Why is this?

Most assisted living facilities don't accept Medicaid. Nursing homes generally have a fixed number of "Medicaid beds" - Medicaid pays less than private pay. So, it's not unusual that you are having trouble with assisted living. That's sad, but the reality of our system.
Carol