Adam, I had a couple of sidelock stocks copied by pantograph and it was anything but easy to then make the finished stocks fit the action as one might have hoped.
There was considerable work needed by a experienced stocker to bring the two together. I used three different people who were time-served stockers at the top of their game and they were all spitting bullets by the time they had the job done.
The problem seems to be mainly that the pantograph works too fast for the wood to stabilise in the process so that it moves and distorts as you work. In some areas they had to let in fillets of wood to correct for the distortion of the wood after the machining. A nightmare!
The guy who did my copying in the USA finally stopped doing shotguns because of this problem and he would leave the job partially inlet for days at a time in an attempt to stabilise the stock as he worked.
Of course, inletting a CNC made, draw bolt, triggerplate O/U is a very different job from a traditionally hand-made, breech bolt, sidelock S/S which is why Perazzi et al can easily CNC a stock to fit but Purdey et al only use a pantograph for the most basic roughing out of replacement stock.
Rifle stocks lend themselves to the process much more than shotguns.
The biggest problem with CNC is you would need a perfect 3D scan of the inletting WITH extra wood left behind in all the key places for the final finishing. And every gun is different so a fresh scan would be required with all the additional tweaks....!