Perhaps the best solution here, would be to have users self-host it, but have each of those plugins talk to one another, and crowd source the monitoring of each others sites. So you never monitor your own site, but request that other sites on the network monitor yours for you. There wouldn't need to be a central site controlling it, but they could all seamlessly interact with each other and monitor themselves automatically.

This could provide some really cool geo-tracking of ping times and load times too. There are services which give information about load times in various placed, but a million websites running the plugin could potentially track a lot more locations. I guess the data would be a bit skewed by them mostly running in mega fast data centers, as opposed to home internet connections, but it could still be useful none the less.