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In order for status pages to be useful, they need to be hosted externally, with no dependencies on the product/system/company they report on.

They're already fairly hard to automate, but making them external makes it even harder. So they're generally not automated. And, hopefully, they're not exercised very often, so they're often forgotten. The best way to manage this, IMHO, is to enable customer service to update the status page and delegate the duty to them. Generally, updating the status page reduces the customer service demand, so CS gets the most direct and timely feedback and is best placed to manage it.

Source: I ran a status page, poorly. It wasn't fully external either, but was far away from all the moving parts, so it would only have correlated failure if our hosting had a multi-site routing issue (which happened once, but not while I was there) or DNS problems, but we had mitigations for DNS not working in the clients, so not too bad.