Well, the main problem with Electron is that every app ships its own browser using tremendous resources at runtime, having huge attack surfaces and lots of unused functionality. So just giving one optimized electron version to all users, certainly does not solve the problem as APE does nothing that changes these problems.
Speaking of deprecating it, it might be one scenario, but developers probably don't just choose Electron because it is platform independent. I mean, there were other frameworks that supported that use-case even before Electron (e.g. QT). However, what is specific to Electron, is that you can use web technologies to build Apps. But that is also nothing you can do with APE.
So as much as I like to see one binary format for many operating systems, I doubt that it will change anything regarding the Electron problem.
There certainly multiple ways of solving it, but in my opinion, Apple and Microsoft must come to a common ground and support some kind of web-view that is built-in to the OS and extended with a platform independent API for the things that normal browsers do not support/allow, like filesystems access.
At some point both supported the Progressive Web App (PWA) movement for a while, but afaik Apple is the one holding it back at the moment. My guess is that they saw their App-Store business at risk. And even if PWAs were a thing, they are still some use-cases they can not cover in the current state (e.g. missing filesystem access).