The traditional post Eisenhower media infrastructure _was_ essentially conservative.

I think your dichotomy here is not left/right but populist/non-populist (aka liberal[1]).

[1] the term liberal has been overloaded for some time now. But it’s important to understand the distinctions. The gist is that most of the deeply conservative thinkers in our post WW2 history believed in a liberal socio-economic order: https://en.m.wikipedia.org/wiki/Economic_liberalism