I explored a similar idea after college as a way to improve textbooks. I haven't done any maintenance in years, but the demo is still online: https://www.okeebo.com/demo/
I found that it was a lot of extra work for authors and they weren't interested.
Since Google search is most likely discovering the AMP page via the <link rel="amphtml"> tag, they really should just use that URL. The Google servers do add a couple minor things beyond being a distributed cache though. First, there's swipe navigation to other articles if the link was located in the top carousel in search results. Second, if you are on a laptop, the Google servers will redirect you to the full version rather than use the AMP cache.
I found that it was a lot of extra work for authors and they weren't interested.