It's definitely possible to use a CNC machine to mill the shape of a rocket engine. You can do some pretty crazy internal milling with a 5-axis machine:

https://youtu.be/RnIvhlKT7SY?t=14s

But the problem isn't the shape of the bell at all. It's that the wall of the bell is not solid, but hollow, filled with plumbing.

http://heroicrelics.org/info/f-1/f-1-thrust-chamber.html

The fuel actually flows through the pipes and voids in the red-hot engine, where it absorbs the heat that would otherwise melt the engine. It then flows back up to be burned.

You'd need an endoscope, not a robot arm, to mill that out!

And neither an endoscope (obviously) nor a robot arm would likely be rigid enough to mill in these materials. Robot arms are typically only used when milling wood, plastic, or soft modeling materials. A CNC mill in metals like the exotic Nobium alloys used in these engines needs incredible rigidity which robot arms just don't have. Consider the hardened tool-steel shafts of the end mills used in the first video - and those are easily broken, while just cutting aluminum!

EBM would work if the tool end could be made sufficiently tiny.

I think you mean EDM, electrical discharge machining. Typical wire EDM usually needs a hole all the way through the material to start, but sinker EDM would work. Interesting idea, wonder if anyone's tried it.

There are edm milling setups. I'm not sure what the major constraints are but I'm assuming the usual: accuracy, cost, repeatbility.

yeah, i was thinking more of an endoscopic robot arm, it would probably need quite a few entry points, and the those holes would need filling again, you could tap those and put a screw it afterwards.

but maybe it's the coming towards end of subtractive manufacture.

I don't think that would be practical. I assume the volume to be milled out is pretty convoluted if you want yo do it mono-bloc. If you break it down, you're back to welding issues.

That said, I'm not a rocket scientist.

I just had an image of a bunch of insect-like robots crawling over and through a giant metal block, chipping away at internal spaces with precision cutting tools to produce the desired shape, carrying away waste material, like an robotic ant colony digging a smooth steel nest.

they wouldn't have to carry anything, you can blow air into the cavity to get the material out. they could have wheels and drive up and down the cramped cavity with a drill on the end. in the end I think additive has won.

You can print voids then flow mill it? https://en.wikipedia.org/wiki/Abrasive_flow_machining