First one that comes to my mind: their advertisers knowing you're on those sites, which page you read, when, for how long, etc. This is mitigated by running an Adblocker and a selective Javascript disabling extension like uMatrix or NoScript, but it would be much better if those sites would let their readers decide if they want to be tracked or not.

Anyway, I'm also blocked on those sites but the same news on LA Times and Fox appear on countless other sites. I'm not losing anything, they're not wasting power and bandwidth for a freeloader. Win/win.