What is your purpose for the rifle? If you want it “murdered out” in all black, obviously you need to paint the barrel in some way. If you want a traditional factory rifle blacked/blued look, then coat the barrel. If you’re going to shoot the piss out of this rifle and burn out the barrel in the next 6months, leave it uncoated.
I do prefer stainless all over, but my current primary match rifle was a “misprint,” I wanted DLC coating on the bolt and inside the action, but they did an all over black DLC. I use either machine finish or bead blasted barrel blanks on the rifle. Since I’m going through two per year, I’m not paying extra cost to finish/coat/paint the barrels.