I'm not sure how email would help. I guess you mean the system would email you once a day saying that the monitoring system is working and if you don't see the email you know to check into it. The monitoring system I use has a higher SLA than 24 hours.
Usually folks divide the monitoring work among two servers and each server monitors the other. Or, you "meta monitor"... a monitoring system that just monitors the monitoring system. Then you get a third-party to monitor that. Then it is turtles all the way down.