AMP specifically disallows JavaScript, so how can AMP "run and behave like a normal app?"
Most of the capabilities of the web are used in a user-hostile way: to annoy, track, or drain the user's battery. PWAs will make the problem worse. AMP is a reaction against this.
AMP will load the PWA in the background. when they interact with the on screen items the PWA will take over. Hence, PWAMPs or Progressive Web AMPs.
as the mobile browser increases in capability it's inevitable we'll see more PWA as it is good enough if not better than native apps in every measurable way unless you absolutely need native app to utilize the full set of hardware on the device or big enough or successful enough that it will be used by millions of people everyday.
Most of the capabilities of the web are used in a user-hostile way: to annoy, track, or drain the user's battery. PWAs will make the problem worse. AMP is a reaction against this.