Well, in most cases this is not the case. Subscriptions don't work but for outlets with passionate niche audiences, or for upper income targeted "high class" outlets. Which leaves most of mainstream media outlets outside. Besides those outlets where ads are peripheral to the main income streams (niche fan supported, paywalled) usually have less ads to begin with.

>What if the site's actually a part of the OS that I've already paid for, but which inexplicably has to be connected to the Internet and serving me ads for Candy Crush?

Well, then it doesn't really need ads.