I agree with you about the good responsive theme that should handle all sorts of device window sizes, but it is not always about the screen or window size. It is about screen size, mobile network capabilities and most important; the user behavior and expectations on mobile.
For instance, I don't think an image slider is necessary on a mobile page. Is it enough to just hide it inside a media query? It is useless to hide something if it is going to load anyway and cause delay. Same for high res images and other network expensive media.
On top of that, user behavior is critical on mobile. You must show them what is key first. They mostly visit a site to do a specific task and leave. And they want to do it as fast as possible.
Same content to some extent is good, but not all content is relevant for a mobile experience. Don't think I am suggesting two different code bases. There is only one web, but it must be flexible.
Yes you can organize the same content different ways depending on the screen size (again media queries), but in case of a CMS like wordpress, you might need different templates to query and show key information at different stages depending on the device.