Unfortunately, that's not the case. MSNBC tends to advocate for liberal positions which, while on the left side of right wing, is still a right wing position. You don't see them advocating much for social democracy let alone more extreme forms of socialism.
If we define left wing in terms of the population as a whole, then there is a huge portion of the population that is opposed to neo-liberal & far right positions and there are no major media organizations that represent them. That's the point that I am attempting to make.