Because to replicate the power of Emacs, you'd need to throw away a lot of privacy/security in the browser. You'd need to let one tab read the contents of another by default. A change to make your mail reading better may break your banking app (yes, that's a reality with Emacs).
Also, Emacs windows vs tabs. Think of having each tab be a non-overlapping window within the browser window.
Finally, most browsers don't let JS code modify the browser itself. If I suddenly decide I'd like Firefox's menu completely rearranged, I don't think JS will give it to me.
If I have two editor tabs open as two browser tabs they should already be able to talk if they're from the same origin, which different editor tabs would be.
The JS code won't be able to modify the browser itself, but neither can ELisp modify the actual Emacs binary code. The customizability in both cases is really coming from an "OS" being implemented in user-controlled scriptspace. You'd have just as much ability to customize that HTML-and-JS OS if it was running in the browser as you have to customize Emacs I think...
> If I have two editor tabs open as two browser tabs they should already be able to talk if they're from the same origin, which different editor tabs would be.
I can interpret your original query two ways:
1. Why can't we replicate Emacs like power in the browser?
2. Why can't we replicate Emacs like power in the browser using existing web sites as apps?
I was answering 2 above. If your mail application is Gmail, then non Google tabs can't read your emails and vice versa.
If you meant it from the perspective of 1, then you can get much further. You'd have to write a generic mail app in JS that can connect via IMAP, etc.
The other headache you'll have to deal with is not having easy access to the disk. Can you easily implement a file manager in JS and run it from the browser? Or access the processes on your computer (e.g. say you want to write a "top" tool for the browser)?
Essentially, the Emacs ecosystem has lots and lots of useful Elisp packages written over the decades. The browser doesn't. And the ones that exist are self contained (i.e. you don't find a JS TODO app that is meant to integrate with someone else's JS Mail app).
And browsers don't have an easy way to install a JS app. How would you do it? Bookmarklet?
As for customizing the browser via JS - yes, you're technically correct. The difference is that much of Emacs is designed to be modifiable via Elisp, whereas that's not the case in most browsers.
So to answer your question, it is technically feasible. You just need a better browser and a lot more people writing client side JS apps.