More one-sided? Most of the big dailies in the USA are already solidly left, editorially. Which way do you see the balance tipping?
The line reporting staff overwhelmingly tend to be left wing. The owners tend to be extreme right wing. Which way the media goes on a particular issue depends on whether it raised to the personal attention of the owners or was left to the staff.
(Fox, of course, changed this by being right wing ownership that tried to make the whole outlet right wing..except for token liberals to provide the losing straw man arguments...)
Peronally, I think this particular line of discussion is useless, with or without a link to some partisan "study" from one side or the other.