More surface area, cools faster.
And because of radial sides, makes barrel stiffer.
Military has found that a fast spiral flute, called a helical flute works much better for full auto weapons.
The helical fluting is CNC machine only.
Strait fluting can be done on any vertical mill, as long as you have an indexing head, or a rotary table, and know how to set everything up.
I've been looking for the right deal on a convex cutter, as I have two very heavy AR10 barrels, and a 10/22 fluted barrel, that the flutes aren't nearly deep enough for my liking.
So I should be able to handle it myself, instead of farming it out pretty soon.
Placing the rifle vertically also cools it quicker as the heat can escape out the bore, while keeping horizontally allows the rising heat to warm the opposite wall.