Not to detract from you comment, but you don't have to have a disability. Some people simply cannot do on-call, disability or not.

I had a co-worker at a previous job, he did two or three on-call rotation and told our boss that he couldn't do it. Mentally it's simply to much for him, especially outside business hours where he felt alone with to much responsibility. In terms of abilities and qualifications he was absolutely able to do the job. Nobody complained or got angry with him over it, because everyone could relate.

At the other end of the scale I had another co-worker, in a more complicated scenario who absolutely didn't care. The payment for the on-call shifts was very good, so he just grabbed as many as possible. He would just take his laptop golfing, no problem. His reasoning: Either he'd know how to fix the problem, if not he'd just to call someone else and hand of the incident.