Guys,
Another reason may be that when you forge a barrel, or any piece of wrought iron, the forging will tend to split at the free end. I call this "broomstraw" splits. When forging I very often plan to cut away the free ends of the piece where these splits occur. With a barrel, if you try to avoid a lot of forge hammering at the free ends of the barrel, than the barrel will tend to take on a shape that is thick at the ends and thin towards the middle. Of course, there is the additional considerations noted above for balance and beauty.
When Remington started roll forging barrels without the weld, barrels became straight sided, early 19th c. After this innovation, most gunsmiths used the straight sided barrels.
Jim