Default Health Monitor HTTPS

You are correct that the default HTTPS health monitor is not particularly useful for testing true application health, since it sends a GET request for whatever the default page is, then will accept ANYTHING as a response, including a 404 Not Found. The HTTPS monitor (along with a lot of other monitors F5 provides) is designed to be customized. You create a new monitor using the HTTPS monitor as the parent, then customize the SEND and RECEIVE string settings (and others) to accurately measure a particular application's health. And you can use different monitors for different applications.