There's really not much solid research that backs up the idea that the press exercise controlling amount of influence on us, despite the fact that everyone seems to think so. The idea was very prevalent in the early C20 but as far as I'm aware has been quite effectively debunked.
There is some research to suggest that the media can have some effect on how suitable we see candidates/parties though, and it certainly does have a very strong 'agenda-setting' role - particularly around election time. As I say, however, most people - politicians included - do seem to be under the impression that media are very powerful, so that does give people like Murdoch more leverage than they should probably have.
Still, all the research I've read has been from the late 80s/early 90s - I don't know how the mass media age has affected the issue.
The idea of imposed impartiality is one I like. I don't agree that it'll lead to uniformity in press - for instance if you passed a regulation that stated that all press had to publish both sides of an argument, there's more than one way to argue for/against something and it would likely increase interest in individual journalists, so the market could still function on that basis.
A free press is a bit like having a free market - it's the best system we've got, but I think it does need careful tweaking to work properly - otherwise you get the crapfest we have now.