They already can: extension authors can specify that their extension only operates on specific URL's.
The problem is that most extensions are designed to work on all web sites, so you have to choose between security and convenience.
Most users pick the latter and trust the former.
This model works pretty well overall since harmful extensions never take long before getting flagged by the community.
No, this model works pretty well for stealthy extensions which take malicious actions without getting detected.
This seems like a good idea until you realize that the behavior you might want to modify is coming from a different domain loaded by the page and you have no control over how they set that up.
Does Chrome not support this? One more reason not to use it.
The non-reddit domains are for expando capability.
This would break adblockers, which are by far the most commonly used extensions
Extensions should be able to have their permissions limited by domain (e.g. to customize YouTube or Reddit) at a minimum.
And I'd also really like a way to track both injected scripts and elements so that they wouldn't be able to make any HTTP requests without additional permissions, not even an <img src="..."> tag if the src isn't just a data URL or local extension resource.
E.g. I want to be able to install an extension that stops YouTube videos from playing as soon as I navigate to the page, without worrying my entire browsing history or worse is being sent to a third-party.