I would be careful about doing that. Other privacy statutes, in the rest of Canada, have provisions that allow individuals to seek damages after it has gone through the Privacy Commissioner process. The courts have generally said that this doesn't actually close the door on the other avenues, but you want to be very careful that it doesn't.
You can see a mechanism.... For example, you mentioned, quite rightly, that the privacy harms are relatively modest when it comes to just general damages, hurt feelings, embarrassment, and things like that. It is seldom worth an individual's effort to hire a lawyer and go to court to recover $5,000's worth of damages.
If you want to enable individual claims on a relatively low threshold in terms of the expense, I think that makes a lot of sense, but if you make it so that it has to go through a complaint to the Privacy Commissioner first, then on, there is no mechanism, for example, in PIPEDA for a kind of a class doing that. One applicant gets to go to the Federal Court in order to get a finding and get damages. You don't want to close the door on that, which would ultimately be a licence to the federal government to commit a huge amount of harm for which it would not be legally responsible.