I think there but the argument in that debate over what is "liberal" news because if you ask a Republican they'll say just about everything as, and to some degree vice versa.
Really to me the biggest difference maker in how conservative media has been able to dominate is total media discipline. Only now are are we seeing some cracks forming but particularly in this past decade is that when Republicans, especially Trump make a statement or a narrative the entire media apparatus picks it up and runs with it, on message. From Fox to the cables to the podcast to the Youtubers, when Trump says a stupid thing and there is a talking point to defend it every single media channel will using that talking point.
It's an advantage Republicans think democrats have but really they don't, not to that degree. Again, Biden was excoriated day in day out by CNN, NBC, CBS, all the "liberal" news outlets were covering every slip up and ran negative stories just as often as positive ones. Jake Tapper wrote a fucking book about Biden's supposed senility.
Republicans can cram it about not having media at least on par with whatever they think liberals have. Again, this argument over the media is pretend, it is the talking point and we keep letting them get away with it.