I don't really see why this required four pages so far. Very few people are in critical positions; even then there is a CoC with acting replacements for a reason. If there is a real operational demand to be on call, you get a phone/pager. If you are on a short notice to deploy (ie, Ready Duty Ship, or RDS in the Navy), then it's a case by case on how far you can go (normally within 4 hours, but it's at the CO's discretion and there is usually a CSO associated with it).
Otherwise having an address or some other way to reach someone outside of normal business hours is fine; very little that can't and the things that can't will normally be all over the news or will justify sending someone to look for you. There is no reason why I or almost anyone else shouldn't be able to unplug and jump in a canoe and toodle around Algonquin park for two weeks with no way to reach me; the system is designed to work regardless.
We are all very little cogs in a very big (Rube Goldberg) machine, and are very replaceable. It's a bit egotistical to think otherwise.
If you want people to be on call, give them something like pagers, and have guidelines about what your expectations are and any limitations (ie stay sober). But expecting everyone to be on call 24/7 is unreasonable and totally unnecessary; folks need their downtime.