I have a rails site, Sensr.net, that adaptively renders on mobile. I'm thinking of AMP enabling the site. We render a mobile version and so AMP makes sense there, but does it make sense for the desktop version of a site?
If you're already running two versions and it works for you, you're probably better off creating an AMP version for mobile only. If you're look to consolidate to one version for easier maintaining purposes, by all means use AMP to create a responsive site that renders on both desktop and mobile.
While the AMP cache isn't part of a Google search on desktop, you will see some performance gains on desktop due to the strict requirements set by AMP that force you to make your site leaner. The JavaScript is also still served up through the AMP CDN on desktop.
The company I work for used AMP as a framework to create a responsive site that runs on AMP for both desktop and mobile (https://www.craigattachments.com). Some of the built in AMP components such as amp-sidebar and amp-carousel made it pretty easy as we didn't have to look else where for solutions.
Here's an article that we found pretty helpful in making our decision to use AMP as a framework versus just a mobile site: https://www.ampproject.org/latest/blog/amping-up-the-amp-framework/.
In particular...
Don’t Let the Name Fool You
AMP stands for “Accelerated Mobile Pages”. In the simplest of terms, it blocks most of the elements which causes the web to load slower on mobile, like large amounts of JavaScript, third-party tracking scripts and bloated CSS. It allows content to almost instantly load. AMP was designed for cached pages, but it is now growing into a broader toolset to fix the mobile web (as the majority of users are mobile today, some site loads still can take minutes). Although the M stands for Mobile, AMP can absolutely help improve loading speeds on any device or browser type.