Sure, a p2p network of people doing distributed pings on a wide range of services sounds like a good idea. Of course, you'd need people willing to run it. A small incentive might be needed... or just a default of "if you want to use this software, you agree to also have your client ping other websites to check if they're up from your location".

But it's not a new idea apparently, a quick search led to https://www.reddit.com/r/selfhosted/comments/1lv9flt/built_a... / https://synthmon.io/home,

How To Build a Botnet 101