The problem there is you'll still always need somebody in the loop, to refill hoppers of parts, to provide stacks of materials, to replace cutters, to watch for jams, etc.
Even large professional shops with stacks of very modern equipment have difficulties with automated parts transfer, and "lights out" manufacturing.
The other problem is that you can't generally just add an arm and manipulator- that can be used to place parts into the machine and remove them from the machine, but you would still need somebody nearby to "hand" pieces in for it to grab, and to remove the pieces it transfers. Or you'd have to also add conveyors or tracks to move the parts around.
And that starts getting complex and expensive. It's worthwhile for big shops doing a large number of nearly-identical items- like auto manufacturers. If you're only making a handful of keyboard, or even just a few hundred, you'll spend twice as long designing, refining, building, troubleshooting and testing the additional feed and follow systems, than it would have taken to just run the parts manually.
A cheaper and easier solution would be to simply add mills. Assuming the job justified the cost, having three mills (or whatever number) working simultaneously obviously gets the job done a great deal faster than using one at a time.