We use and sell calcium carbonate as a blasting material. It is harder than soda and also more productive. Our coarse calcium carbonate can actually strip mill scale.
It's a dusty material and can leave chalky impregnations in the substrate. However in my experience it's quite a good material for non porous, flat surfaces, making a surface profile that is barely noticeable even when blasting at around 60 psi.
We use it to restore marble graves here. I recommend it to my customers as a cheaper alternative to soda. Also, I'm no chemist but I never really liked the idea of blasting surfaces with hygroscopic salt.