In other ways it doesn't (depending on the techniques). Things like metallurgical resistance, defect creation and tolerances
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!
but maybe it's the coming towards end of subtractive manufacture.
That said, I'm not a rocket scientist.
It makes sense. Rocket engines are mostly a big single piece with lots of internal voids. The fuel is used as a coolant, so there are channels inside the engine bell and some other sections. It's mostly plumbing.
That's the kind of part where 3D printing is useful. Making a big object with internal plumbing out of multiple parts is a fabrication headache. NASA's engines have vast amounts of welding work in them. High-pressure joints are always a problem. Making something with few or no joints is just better. It still has to be inspected, but that's what industrial-sized CAT scanners are for.
(Most of the real-world problems in both rockets and nuclear power involve plumbing and welding.)