R.J.
In our area, that's because most people who *need* night/weekend care and don't have someone at home to do it are on the edge of poverty... and therefore living in bad areas.
What I did? (for a year when I had no help, nightshift, no weekends) Paid college kids $20 a night + home cooked dinner leftovers. They came to my home and got paid to have a quiet place to study and real food. Beat the hail out of noisy dorms. Sophmores were my bread and butter. Got all their wiggles out as freshmen, but can't yet afford to move off campus. My shifts worked out that I put my son to bed before they got there. Most of the time, they never even saw/interacted with him (I did have a nanny cam in his room that I never mentioned). Because my son could sleep through the second coming, if they didn't have a car I often drove them home (just popped my son in his carseat), or they were welcome to crash on the couch and catch the bus in the morning (ditto if they drove). They usually chose to go home, since my son would wake up / our day started very early. Met some REALLY great people this way.
I just posted a notice on the dorm's message boards outlining the job, hours, days needed, and pay (I only "required" 1 day a week). Then I interviewed. Always had tons of applicants is desperate need of a quiet place to study.
$20 a night is SUPER cheap for our area, since it's usually $10 per hour.