The fact that a status page is not reachable would itself imply the status of the service whose status it reports, no? Especially since visiting the status page is not normally done unless someone is having problems with the service.
Not really; part of the point of a status page is that it lets you distinguish between "their service is down" and "the route between me and their service is down".
I wonder if a static page on Netlify would comply with their privacy stance.