We could run the code in a chroot environment that simulates the whole machine. It would be a safe place to play. We could call it something cute like "sandbox." Naturally it would be resource limited so code couldn't consume all your memory or CPU cycles. That would be completely under user control. People might want code to show ads, but the user could limit them to 100 ms of load time, 5 seconds of wall clock time, and no more than 10% of the screen.

What browser would go to great lengths to implement such a sandbox to run a code which the user does not care about and for which they have no use anyway?

People put "no ads" signs on their mail boxes. Do you really think they'd see such a thing as a feature? Crazy stuff, no browser on their right mind would shoot themselves such a bullet in the foot. People would immediately turn to the competition, should such a thing happen.

What next? Document viewers weighting several megabytes? Containing a full-fledged garbage collector?

I'd say let's keep things simple. People like simplicity, and stuff that works and that does not freeze or crash every other hour.