Sure, liberals have been criticising Google and Facebook recently over the Trump/Russia stuff and about their ability to influence elections, but only once Trump and Brexit happened. I'm not sure they cared all that much before, at least not beyond specific issues that were mostly confined to the tech sections of sites like the NYT or Guardian, or generic 'big corp' stuff like tax avoidance. The Daily Mail and the Sun have been running sensational front page stories about things like David Cameron having close links to Google or Google making it easy for terrorists to build a bomb for something like 5 years.
The reason I mention right wing politics is firstly that they are the ones in power at the moment in the US/UK/Australia - Trump and May aren't going to care what the Guardian or NYT say and don't have any ideological reason to care about things like the immorality of online advertising or the affect of social media on mental health. Secondly, in the UK at least, the press as a whole is much more closely aligned to the conservative political parties. The UK press is divided roughly into right wing (Sun, Mail, Express, Telegraph, Times, Spectator), liberal (Guardian, New Statesman, FT, Economist) and left wing (Mirror, at times). The right wing outlets have vastly higher readership and reach. So if the media does have an influence on politics, it's going to be in one direction.
But my point really was that it's interesting to me to see how much the papers are working for the right wing parties or how much the right wing parties are following the agenda set by the newspapers. That's probably not so much a thing in the US (although the same question about Fox might be), but it is in the UK, especially at the moment.
E: also, to be clear, the same financial inceptives apply to the NYT and Guardian - online advertising is killing their revenue streams as well. It's just that as I said they have limited power at the moment (and it's arguable how much power they ever have - neither seems to have the ability to set the news agenda outside of the liberal middle class bubble, unlike the UK tabloids for example).