Earlier quoted context omitted.
If you can write a perfect automated status page - can't you basically write perfect integration tests and make sure no bad code gets deployed? Bit of a chicken and an egg problem :)
Do you write every single test for your codebase? Do you have control over every line of code that gets deployed? The purpose of monitoring is to detect issues, because preventing them entirely is next to impossible. By your logic if you can write perfect integration tests, can't you write perfect application code that doesn't need to be tested?
1) A guy with a button. It's right, but it requires the guy to notice or get told - and remember to push the button.
2) Automation. But your automation has to somehow catch bugs that you can't even dream of. And not be triggered randomly. And somehow be able to be automated but not fixed at the source (as if you know how something will fail - why not just fix that over adding more status checks?)