I think they relaxed that restriction long ago, hence the variety of browsers, email clients etc available.

I was under the impression that things like browser apps are still just wrapping UIWebViews and such. I know this is the case for Chrome - the (heh) chrome is different, but the browser itself is the iOS stock. Is it a technical restriction rather than a philosophical one?

Both. Apple has a restriction on 'executing' downloaded code yourself (javascript).