My guess is owning the user time, e.g if you read article via AMP you don't even visit the original website anymore. Same with providing answers directly in the search results.
The long term benefits are that they stem the bleeding of everything moving inside mobile apps. They need content on the web to remain useful and developers have shown they're unable to make good mobile experiences themselves.
I think this particular move is more tactical than strategic. I think it provides a better experience for users and keeps Pinterest, one of the main AMP users, happy with Google.
Get 'em hooked on something 'free', then monetize it. Rinse and repeat. Just like they are building a browser that only blocks the 'annoying ads', now they are designing their email to let advertising through. So much for 'don't be evil'.
Things can be both monetized and 'free' and I don't think it necessarily has to be evil simply therefore. What I'm curious about is how they intend/could monetize it?
AMP is afaik an open web format, what's the "get 'em hooked" part here? Is it just a defensive play against Facebook's Instant Articles?