The key technique that AMP promises will beat the limits of network latency is precaching. Unfortunately, users have a strong privacy expectation that random websites will not be notified that you are interested in them until you actually click the link in search results (or news, or whatever). For precaching to work without violating user privacy, the data needs to be loaded from some server that already knows that the link was shown to you, so there is no privacy violation from giving it that information. AMP's solution is for the host company of the results page to fill that role.
The AMP lightning bolt is intended to mean "this page is already downloaded offline on your device, and so will load instantly", not just "this page is well-designed and fast". The difference is minor for blazing fast connections, but that isn't true for developing world users with weak connections and devices.
Google has said that when open web standards like Web Packaging finally show up which enable the same safe preloading behavior, those sites will be included in AMP carousels. We'll see whether they follow through with that. [1] [2]
* All experiments conducted with cache disabled, times are until Load event fires.
[1] https://blog.amp.dev/2018/03/08/standardizing-lessons-learne...
[2] https://github.com/ampproject/amphtml/blob/master/contributi...