Do you think you will be able to tap the threads in the nut faster on a CNC than a 1" NC tap? Dropouts video shows the way it is done on a milling machine. Those will be for high tech parts where you have unique tolerance spec (expensive). You need to pay close attention to the fixture they are using and then think about the quantity you need to make. If you are talking very small quantities (say <10 - 20 per run) then this might work, but if larger quantities are needed I am not sure you will be happy with the speed of a typical 3 axis CNC. It would eliminate the manual labor, so that might what is most important to you.
If you want to see how they fixture larger batches of unique small parts in the milling world this link might give you some ideas what is involved: https://www.cnccookbook.com/cnc-jigs-fixtures-workholding-solutions-milling/
I am not sure if the process to thread the dowels will be incredibly fast either on a CNC with a 4th axis. If you can accurately locate a 1" rod and simply mill in the threads, maybe, but I would be doing some research if this is important to you before plunking down money for a fourth axis.
It is easy to think you can do endless things with a 3 axis CNC, and honestly with ingenuity you can in many cases. The question comes down to, does it make good sense for a business application?
Are you sure there is not a supplier out there to supply this part? Markup on a supplied item works out well for some products.
https://nuts-bolts-things.com/product/nut-bolt-washer-set/
These guys have threaded rod, but no nuts. This link is for 3/4", but I bet they could supply 1".
http://www.architecturals.net/threaded-dowel-rod-34-maple/