A 16gram C02 will totally fill a 23c tire. I know that 20pumps with my Lyzene Road pump plus a 16gram will fill my 25c tire perfectly. I carry C02 and a pump because there are times when C02 is very handy. Once, in some rain, I got a slowww leak. I could have changed the tire but the rain was cold and I had a C02 cartridge so I could just give it a short blast, ride for 20min, add a bit of air, ride for 20min...do this three or four times and I as home without having to stop and change my inner tube. On a ride with friends I prefer a quick inflation with C02 so I don't hold folks up any more than necessary. Same when mosquitos are driving me crazy. Other times I maybe in no hurry and I'll just pump my tire up. Having both doesn't bother me in terms of weight or space so that's what I do.
BTW, at a recent race a fellow "helped" top off a buddy with a somewhat underinflated tire and blew it out with C02. It made a huge "boom" and scared the pee out of everyone nearby. The resulting commentary among those involved was humorous to listen to .