The show's remit is entirely entertainment.
The problem with giving the public a vote - and the parallel is Ali G over on X-Factor - is that the public is prone to be wilfully mischievous with its voting powers, which increases the profile of the shows, and vexes anyone with anything approaching a moral sense of fair play.
I think the job of choosing a selection of people who are not only nominally famous, but also have no dance skills would be pretty tricky, not to say unentertaining.
One Ed Balls, the same as one Ali G per serious makes for controversy - a bunch of them would make for boring television, which defeats the main remit of either snow.