Having tried it both ways, certainly CO2 makes life a lot easier.
If you have lots of space then the idea mentioned above of keeping many cultures on the go probably avoids the need for CO2 for our purposes.
However if, as I am, you are space limited, you can bring a culture up to density in 2 or 3 days which can quite literally be a life saver.
The BIG advantage to me of using CO2 is because I now have a second CO2 cylinder and support equipment. I have a tank full of SPS and without the Ca reactor, Ca and alkalinity drops frighteningly quickly. If the Ca reactor's CO2 runs out, not a problem. The phyto can easily cope for a few days without CO2 whereas the coral sulk pretty quickly. The extra security of having a backup system to the Ca reactors means that the only real cost incurred specifically for the phyto was a pH probe to plug into my aquarium computer.
I guess that means getting CO2 for phyto growing is a reasonable idea, but it’s a great idea if you have other uses for CO2 within your aquarium setup.
FWIW