The lathe can indeed make a finely shaped barrel and even make it appear extremly smooth. But in reality it comes off the lathe with a surface like screw threads, extremely fine and microscopic screw threads.

The striker may indeed draw file and shape the barrel to it's required form. That's how many of the oval barrels with integeral ribs were made. But the striker won't stop with filing. The striker will also hand polish the metal with polishing compounds or strike the metal with burnishing rods to further smooth the barrel and remove the file marks.