This is in fact how PWAs work on iOS. They do not run in Safari at all, but in a special runtime called Web.app, which is coded to use WebKit. Safari doesn’t have the ability to do the things the PWA runtime can do. Letting other browsers “run PWAs” would not be a matter of exposing an existing private API, it would require creating a a brand new plugin API for Web.app that would allow inserting other browser engines into it.