don't groups open up too much during prolonged fire to make a lightweight barrel truly practical?
For 2MOA combat use, no.
For high tier competitive use in position square range shooting, maybe.
In combat, you have to carry it miles across country to even get to the place where you shoot - if the enemy doesn't come knocking on your door - and even at that, if you are expending a magazine a minute in a firefight, practical accuracy is well below minute of man. A heavy barrel is of no value in that scenario.
Position shooting on a range, IF there is a rapid fire string, then, maybe. What the proponents of heavy barrels are saying is that the mass of the barrel absorbs more heat which keeps the overall shape of the barrel from distorting.
If the barrel is distorting from heat, then it is because the material isn't homogeneous and has flaws, inclusions, and stresses in it. That is an admission the blank itself wasn't very high quality. In fact, doing a great job rifling it would be a waste of effort if it's going to drift all over creation just because it warmed up. Better to spend the money in a higher quality stick of metal that was formed with processes that prevent it.
If anything, that's what you get with the $400 barrels that come with a guarantee. Spending another $40 for the option won't get you much in the way of improvement except looks and bragging rights until you prove it actually gets you a smaller group.
With barrels made by mass production techniques pouring off the machines, good luck with that - the profile is cut last as a cosmetic feature. Plenty of pencil and recon profiles do very well in accuracy - the blank is well made, few inclusions, came off the line straight and wasn't bent to force it that way, had great drilling and rifling, air gauges to a high standard.
Yes, they actually bend them cold to straighten them. That's how you "regulate" a shotgun to hit point of aim, too. Yes - bend it.
You have to pay for an accurate barrel, or you take your chances. A heavy profile in and of itself means very little - unless you are humping it ten miles a day cross country, at which point it's highly impractical.
Just another one of those things that sells because it can be, not because it's proven to work.