Companies 1/1000th the size of Amazon can manage it.
But the last thing you want to do is put inaccurate information onto a status page; so mere administrative personnel isn't enough -- you'd need people who understand enough about the system to be able to write about it without introducing errors.
I'm guessing that the intersection of "administrative personnel", "willing to carry pagers" and "understand the internals of AWS services" is a very small set.
Not every job can be full of self-directed aspirational spiritual awakenings. If that were the case, nobody would deliver my dinner on a bike when it's -20ºF outside.
Being a non-engineer doesn't mean they don't know anything about the technology. And they don't need to know the internals, just enough to convey information from the engineers managers to the public.
Plenty of other organizations manage resolving issues while transmitting information about the issue to other stakeholders.
Also, most administrative personnel have far less job opportunities than engineers. If they can get the engineers to carry pagers they can get a PR minion to carry one.
They also claim to have "customer obsession" as a leadership principle, this whole thread is an excellent example of that being failed in a big way.