Having some uptime monitoring at the website level would be extremely handy for many of us. It could even be a service level differentiator!
For example: I am evaluating switching to ClientExec and have a demo site setup for it. While attempting an import of data the website container became unstable and unavailable and ended up in a 5XX state. In this case I was aware of it but in a production environment a website may go down and being able to have this monitored at the Control Panel level would be awesome.