What happens when you leave the cannon? Either the cannon exit is near ground level, in which case you still have the air resistance problems; or it's not, in which case you have the problems of building very a tall cannon.
you don't have to exit the cannon at high speed, the v^2 drag will kill you. You're just trying to put some kinetic energy in the rocket in a way that doesn't make you carry it. you don't have to put all the energy in it that way, the current system works, it's just a tentative improvement.
But your answer makes me feel you've not seen the ping pong ball cannons, because they have very good results with a very low mass.