In the context that the question was asked, several reasons.
First, Spyktr said that "any CNC" shop might now be a viable gun mfgr. If you can't feasibly make barrels, it's more like "any CNC shop can be a 90% gun manufacturer" (which is not a problem, some of the well known names buy their barrels outside).
Second, if the topic is making something yourself because the regulatory climate is different or you desire to be self sufficent, and there is one part that's harder to make than the others, it's natural for that part to become the focus of your attention.
Third, trade in most gun parts is pretty unregulated, as you say, but as you might expect, BATFE or someone has selected one part and said that this part is still a gun even before assembly with the other parts. This makes sense if you accept for the sake of argument that the government can regulate manufacture/purchase/use of guns, because otherwise people would just order all the parts, assemble them themselves and get out from under the regs. The same thing is done in cars. If you completely tear down a car, the front firewall is the part that's still the "car" and that's what bears the VIN. Up till now that part for guns has been the receiver, which leads to the final reason for the question. If you were BATFE and you saw a bunch of guys machining their own receivers and thus exempt from most regulation and you (being a tyrant who had to drink from a bottle as a baby) don't like it, what's the next logical step? Control the part that's hard to make, thus making it a choke point in the process. If I were BATFE, I'd be thinking the wrong part of the gun has the serial number.
Now bear in mind that that didn’t amount to a complete rebuttal of Spktyr’s statement that this would make gun manufacturing attractive to a broader group of shops and individuals. Even if barrels do prove to be too hard for a non-specialist to make, if there are a significant number of shops and individuals who can make everything else and want to do so, then a market forms for a barrel maker to move to Alaska or set up from scratch, thus bringing us back to the “entirely made in Alaska” premise that the thread is about.
I would agree that making a good rifled barrel would be more of a challenge than would be making a servicable receiver.
Interesting shop. Over 1/2 the rifles had suppressors. One was an old Delisle (sp) from WW2 that was converted from an Enfield. Neat toy and very quiet. The owner was kind enough to let me take lots of notes and pics of the insides.