It's very easy, except when it's hard. Also, it's never easy.

Joking, but only somewhat. That's because the easy cases are handled by automation, etc. If you knew it could happen, you probably planned for it. Figuring out what the issue is, if there really is an issue, and the scope of the issue can take some time.

No. “Doesn’t respond for me” doesn’t imply “down for lots of people”. If you discover that foo.com doesn’t respond, it takes a while to figure out whether that’s on your system, in your network, in the city, etc.

Yes, you would set up multiple hosts across the world polling that server, but that adds complexity. Maybe, those pollers decide the site is down because of a bug in your network setup, while the rest of the world happily uses your services.