The value is that when support staff has real phone numbers available to them, they tend to dial historically responsive individuals directly in order to get a problem resolved, thus creating a negative feedback loop -- if you ignore notifications and phone calls, you get called less by support staff in the future.
Having a floating number -- especially if we could get statistics on who answers and who always ignores them, and if the number could "call up the chain" automatically when nobody answers, would be a useful tool to solve this issue.
Of course, the preference is that human staff doesn't need to call anyone, but it still happens.
That's an interesting idea. We've actually thought a bit about adding phone-based triggering to PagerDuty (via a 1-800 number + access code). The idea was to make PagerDuty useful to non-IT businesses like plumbers that also have the concept of out-of-hours on-call duty. From your comment, though, it sounds like this kind of feature would be pretty useful even in the IT world.