Narrow kerf chain does cut faster, but has some limitations. They are designed for smaller saws and have less stressful cutting. Milling puts quite a strain on both saw and chain. Narrow kerf chain, such as Stihl Pico, will break while milling with a large saw. Sharpening is also a consideration.
Smaller cutters mean less tooth to be ground away.
You can only sharpen so many times before the tooth is gone. Another limitation to narrow kerf chain is that as you remove the teeth when sharpening, the cutters become narrower than the saw bar. Even with a narrow bar. When this happens, the chain is useless because it can't cut into the wood. If you are not sawing for production, kerf is really not a concern.