To me the danger seems to be not in the randomness of the code, but that it can run without the user's prompting or consent. Perhaps it would be a good idea for browsers to disable JS JIT by default (as this is where a large percentage of holes crop up) and allow the user to enable it where they find the benefit low-risk and worthwhile (e.g. with vetted web apps).

The downside is that the web is a bit slower by default, but that might not necessarily be such a bad thing and encourage more developer consciousness of how much JS they're pulling in and how resource intensive it is.