Weird I would expect that iOS sandboxes apps in such a way that it doesn't have any impact on other parts of the phone even if the app is hacked.
But I don't see why a browser should run at system level - if the app is closed, there is no reason for its code to be running.
It definitely does not need to run all the time, it could be woken up by incoming notification like all other apps (and I hope it is how it actually works).