So you can maybe ship Gecko + SpiderMonkey, as long as you only run JS that's part of your app. But if you want to run JS from a website (or indeed any code from anywhere), you're not allowed to do that on iOS.
I haven't checked whether it would be OK to ship a browser engine that doesn't support JS at all, but that's a fairly academic question anyway.
I guess what's bothering me is that there is an unstated assumption underlying this entire discussion which people never bring up: for performance reasons, the rendering engine has to be tied closely to the JS implementation. Specifically, calling over some IPC interface at every entrypoint into the JS interpreter would be a performance nightmare. This is the reason why these can't be disentangled. The connection to the interpreter is really an indirect one.
That is not true. Many apps do this. Games have been doing this for a decade. It is not a problem to do this. Apple has never made a big deal of that. Only if you are trying to build a shadow app store.
Apple does not care. As long as you are operating in the spirit of their App Store.
You know when they care? When you start charging money for those downloads. Via an alternative payment channel. Or when you run an alternative app store from within your app.
If you download assets on demand, and some of those turn out to be executable* code, nobody cares.
* Where executable means 'interpreted' because you cannot run unsigned code. But for games that is fine, they have been doing this with JS, Lua and Python for a decade.
(You can downvote me - but this is based on a decade of experience)
The subject we're talking about here would not fly under their radar.
Pebble used this quite effectively to add phone-side apps to their product.