Just being charitable here (to be clear I agree with you) - but I think a big contributor to a lot of folks taking these old media organizations more seriously than they should, is how batshit insane the rest of the media ecosystem has gotten.
That combined with the kind of...legacy of trust, for these old "household name" ones? It's hard for us olds to update our mental models in a deep way. I was raised thinking it was a respectable outfit - I know, for sure, that I don't trust them or like them at all today. And yet every time I see "New York Times" my subconscious goes "ah, yep, one of the good ones". Brains are dumb and annoying.