What the axis' are called is irrelevant. Has anyone tried pocketing with a 3 axis lathe?
I think the part that you're missing is that 3 axis won't do it. At least not both parts and pockets that will actually fit each other.
The issue is that you must offset for the cutter diameter in a separate axis. Without this, the parts and the pockets will have walls at different angles and will not fit each other.
Let's look at it from a standard 3 axis lathe configuration.
X axis moves the tool across the spindle center line. It would account for diameters when turning and pocket depth in your scenario
Z axis moves in line with the spindle center line. It controls the length of turned parts, or would account for the lengthwise straight linear component in your scenario.
C axis is the rotation of the spindle, and the ability to index it or control it with the same accuracy as the other axis'. The C axis would spin your parts during turning, or account for the second axis of cutting in your scenario. The one perpendicular (sort of) to the Z axis.
What is missing here is the ability to raise and lower the live tool spindle holding your end mill. Without it, you can't get the side of the end mill on the cut line, only the center.
Once you have the ability to offset the cutter, then you have to program it. As far as I know, only the higher end software packages offer true 4 axis interpolation. And they usually have a very strong learning curve.
So, while the idea could work, it would require more than you suspect, and would not provide anything substantially different than what is already done with much simpler and less costly means.
Take a look at our Infinity Inlays in this cue: (Hover over the pic to get a zoom window)
http://www.obcues.com/products/OB%252d135-Darts-High-Performance-Pool-Cue-with-an-OB-Plus-Shaft.html
These are all inlays, not splices. There are not little holes or gaps filled with epoxy to hide the fixes, and they are not hand carved to make them sharp. They are all done on 3 axis gantry routers.
I have 3 commercial CNC lathes. We use them for making rings, collars and butt caps. We also use them for end work like ferrules and ferrule tenons, installing cutting and shaping tips, and machining the joint ends both cues and shafts as well as the butt end on our cues. I don't have C axis on any of them, and if I did, I still wouldn't even attempt making inlays on them. I have been exactly where you're at and asked myself the same questions you're asking here. But, after I learned much more about it, I realized that it just wasn't the right way to do it.
I hope that helps!
Royce Bunnell
www.obcues.com