I have a Desert Tech, so I may be biased. I haven't used an AI, but will someday.
In regards to the barrel cost - the barrel cost is the barrel cost. Smith''s charges are similar. It's the barrel extension that puts a DT barrel at a ~$300 premium over the next manufacturers barrel. But once you have the barrel extension, the cost is all the same, whether its an AI or another custom, and the barrel extension can be used on your next barrel.
There are lots of smiths that can cut a barrel for you. DMR in Vegas, ES Tactical, TS Customs, SAC, SPR to name a few. I can call any number of them up today and get a finished barrel in 2-3 weeks if I need to. Hell I can go to
www.es-tactical.com and order one right off the website and it will show up and my door and drop into my chassis. I am sure that Mike @ Mile High wouldn't mind assembling a DT barrel either (lots of SH Podcast entering my earholes lately).
However it seems that more and more people are requesting switch barrel designs, so when the market needs it, someone will create it. Isnt that why the Bugnut was created by SPR and the Barloc was created by ARC?
ES Tactical -
https://www.es-tactical.com/shop/Desert-Tech/ES-Tactical-SRS-Barrels--Conversion-Kits.htm
Southern Precision Rifles Bugnut -
https://www.bugholes.com/category-s/1820.htm
American Rifle Company Barloc -
https://www.americanrifle.com/product/barloc-quick-change-barrel-device-for-barrels-with-shoulders/
@OP - to address your last question "Why hasn't a custom action manufacturer made an action that will take the same AXMC barrels?" With the Bugnut or the Barloc, that's possible with the action you may already have that uses their own threads. Now it is 60 or 120 second barrel changes like the DT or AI? Maybe not, but I have zero
need to change a barrel in 60 seconds, and would be perfectly happy with another method if I wasn't already spoiled with a torque wrench as the tool to make barrel changes.