Theoretically, browsers could even stop from the JS engine from being started for the site in the first place.

The NoScript extension is basically this. Most of the client side stuff is off by default and you can enable it per-domain. It breaks a whole lot of websites, but often in ways where the main content of a website is still readable. Over time, you can build up a list of “allow by default” domains and most of the web you care about works. Though, you may have to spend a moment or two sorting out permissions when you visit a new site.