I'm in favour of getting rid of the passing-through-schools bit, not because I think it will level the playing field but because a few people I have known have been royally screwed by the multi-tiered process. In one case, three of the department's top five candidates (including numbers 1 and 2) were NOT forwarded to Ottawa after the rankings were ignored by the faculty of graduate studies. The professors were pretty angry and there were meetings and complaints and handwringing but nothing ever actually happened with it--grad studies sort of said "Yes, we screwed up" in the private meetings with students and professors, and then publicly released a document that said they did the right thing. Of the others who were not in the department's top five who got forwarded on, none of them won a SSHRC. The others who were in the top five did. This case isn't so much a problem with applying through schools but rather a problem with schools that seem to misunderstand the system when applications get to SSHRC.
At the same time, though, people who are at university's have a big leg up just from the fact that they can consult with professors and develop their applications with much more one-on-one feedback. I'd feel far less confident in my own application if I hadn't gone through 14 drafts or so, getting feedback from a variety of profs on each.