I'm a bit confused about the necessity for finned tubing, or how it equates to a radiator.

If you already had a lot of radiator surface area (which in a custom loop, you should) there would probably be very little difference. why reinvent the wheel since radiators already do a great job? not only would this be difficult to get right, you probably couldn't bend the tubing as well if you put fins all over it. There are lower limits to how cold your loop temps can be (just above ambient is the lowest in a conventional water loop). If you want lower temps, add a radiator to get it closer to ambient and maybe a better pump. if you want really fun temps, you will need to chill the water somehow.
As it turns out, I do have access to a friend's CNC rig, but I'm confident that this is impractical. good idea, but not worth it.

As it has been said before no need to reinvent the wheel and adding fins to heatpipes would do basically nothing given how most of the heatpipe is covered up by the heatsink.

You could, but alum fins would be better for air cooling. And you would be dropping heat inside the case right? Though not a lot so yes I think it would work, I think they don't just because that is what the radiator is for and its more work, would look different, etc.

Take a look at large ~5hp air compressors, a lot of them use a tube with fins behind the flywheel to cool the air between stages. Is that the kind of thing you mean sort of?

The last part is its hard to cut tiny fins in CNC, that is why most are extrusions. Have to use a small cutter so its slower and they like to break, unless you get a specialty cutter like a saw blade looking thing. Even after you pay for that, cuts are sharp and its work to debur it. On other hand it would be really easy to make a water block in a CNC. I have a trans cooler on my car and seems like that would make a good loop cooler, or a heater core, but yes they would be ugly.