Sites like PhotoPea and Google Docs capture right-click to offer right-click menus more in line with what you'd expect from a desktop application. You could argue that other UX schemes can work without that, but since that's what a lot of people are used to, I'd say they count as valid use cases.

One example would be a browser game where left click places a block and right click removes a block. You wouldn't want the default context menu appearing every time you right-clicked.