If WaPo or any other news publication decided to turn off ads out of moral obligation to prove a point, they'd be digging their own graves. You're essentially arguing that they should commit economic suicide if they truly care about ad tracking. Our culture isn't willing to spend as much on news content as we do Netflix, and that's just a sad reality.
Facebook, Youtube, etc. OTOH have built very profitable advertising systems that form the foundation of their entire business. They fully control these ad networks and all their data. And in this case, it sounds like YouTube may have violated COPPA, which is a totally different level of moral failure than choosing to put up ads.