No, a traditional newspaper optimizes for number of subscribers/readers, not for time spent reading the newspaper. It's online ads that change the equation.

Traditional newspapers all rely on online ads these days

Exactly. For-profit social media and news media are both chock-full of perverse incentives.

The only solution I can think of is to somehow promote the use of non-profit providers, but I know of no good/usable ones in either case. For news, there are individual, independent bloggers, and for social media there are closed chat groups or something, but that's about it.

That's not the solution at all. Many of current media like Breitbart/Fox as well CNN/MSNBC leverage a fundamental bug in human psyche: emotional and shocking content keeps our attention! So these media try to hype/spice/misinform as long as it gets attention. You cannot counteract it by non-profits providing boring news.

I don't know if there is any solution at all. I expect both sides to maximize spiced up news delivery for maximal attention and devotee base. At equilibrium, we may have these equally weighted strong groups which may randomly win election by small margin each time. This might not be too bad because over longer term all decisions and laws would be averaged out over two opposing philosophies resulting in overall centrist and balanced system.

It'd certainly be a start if there were at least some good alternatives for people to use. It wouldn't solve the problem, but at least there'd be an opening for norms and viewing habits to change a little.