Yes, the browser's same-origin policy is why the webapp has its own API root. There's no problem with casually using the web service from your web browser. The thinking behind our desire for a detailed breakdown of non-browser clients is because their behavior is less predictable than browser clients. If you write a program that 100,000 people use and it turns out to have a huge bandwidth-sucking bug, we want to be able to throttle usage of that program.
Yes, the browser's same-origin policy is why the webapp has its own API root. There's no problem with casually using the web service from your web browser. The thinking behind our desire for a detailed breakdown of non-browser clients is because their behavior is less predictable than browser clients. If you write a program that 100,000 people use and it turns out to have a huge bandwidth-sucking bug, we want to be able to throttle usage of that program.