I know there are plenty of services to redirect normal pages to mobile versions when viewed on a phone/tablet, but shouldn't the mobile ones be able to check for desktop browsers and make the reverse switch?
Because until the last couple years, mobile was a second class citizen. A vast majority of the web is still desktop first, and therefore, the expected and default view. The trend that reverses this will likely be a mobile-first responsive design, where the site scales up automatically on the clientside.