I've seen sites that refuse to show you their content at all until you've enabled notifications. I like this lying idea.

I feel like a good extension to make would be a lying extension. Make it able to lie to a site about any API and have set configurations to deal with specific types of behavior.

I don't understand why browsers would ever not lie about this.

I feel like if a specific browser, ie. Firefox went down this path, it wouldn't take long until websites stopped supporting that browser. It'd take browser wide action to take on big players such as Slack imo.