In the Prussian army after 1808 (and probably before as well) men without front teeth were considered unfit for military service.
I guess, this was just for aesthetic reasons, as I can definitely confirm from over 20 years of re-enactment as a Napoleonic infantryman that you do not need the front teeth for biting off the cartridge.
On the contrary, if your front teeth are not so good and the paper too strong, you might loose them by biting the cartridge with them.
With the sideteeth you can exercise much more power on the paper - just fold a piece of paper and try to bite off part of it yourself.
PS. I just heard an additonal explanation - hearsay, allegedly from a dentist: If your front teeth are missing, the side teeth will get loose soon, as they are no longer stabilised by the front teeth ...