There are some valid concerns about fluting a barrel. Depending on how the barrel is made there are residual stresses left in it. Hammer forging (Sako, Tikka, CZ, & some Remingtons) probably leaves the most residual stress. Button (Shilen, Lilja, Hart, and many others) rifling is next, and cut rifled (Krieger, Bartlein, ...) the least. The issue is that when you cut slots in the barrel OD you release some of the stresses. This can do at least a couple of things. First, the barrel can simply distort and bend. Some barrel makers straighten their barrels in the factory. Second since you are releasing stress, the bore of the barrel can increase in diameter. Hart, and I suspect others, manage that issue by leaving the final hand lapping of the barrel (which removes as much as 0.001" until after the fluting. That way they can restore uniformity to the bore.
The other issue besides residual stress is the thickness of the barrel. Increased bore (like a 30-06 vs a .223), cuts into thickness, as does a lighter profile on the barrel. So flutes in a light sporter barrel with a big bore can be trouble. Most barrel makers set a limit on the thickness profile that they will not go below and flute.
But flutes do look good, and especially on a heavy barrel take away that piece of pipe look.