Interesting. I can see how the materials might be a challenge, but not sure why size should be over the long term and at the scales required for watches.
Many parts in a watch are actually sub-assemblies. Even a simple train wheel in a good quality watch has Glucydur typically (an alloy with very specific properties) for the wheel, and hardened steel for the pinion. If you could even print those materials separately, they would still require post processing operations to achieve proper surface finish (critical), and then be assembled/staked together, part trued, etc.
More complex parts are a bigger challenge - take a balance wheel:
This is a simple one, so it consists of the balance (Glucydur), the collet, the balance spring (Anachron - another very specific alloy and it's welded to the collet in this case), the stud (balance spring is glued to the stud in this case), the balance staff, and on the other side the roller table, and the roller jewel. They are almost all different materials with very specific engineering properties.
They of course can be more complex, like this one:
Now we have an overcoil on the balance spring, plus screws on the balance for posing and different screws for timing. Now I don't replace a balance complete everyday, so what about something that I replace all the time, like a reversing wheel?
As you can see it's referred to as a single part, but it has two wheels, a series of ratchet/pawl mechanisms inside, plus a couple of jewels. Even if I could print all the individual parts, assembling this would be a challenge since the entire assembly is about 4 mm in diameter.
It's not an impossible thing to print some parts that are in a watch certainly, as some are very simple parts like flat springs or other stamped parts. But in these threads where additive manufacturing is cited as the cure-all, the idea that is often floated that everyone will have a printer at home where they can simply print a replacement part and drop it in the movement. That is far from reality at this time.
A watchmaker in the UK recently studied this and had sample parts 3D printed, working with a company that specializes in printing in metals, and they were no where near being satisfactory for use. Biggest problem to even starting testing of these parts was the surface finish - it was no where near the level required for watch parts. The printing resolution is just not at this level yet, and getting that is only the start of the challenges. Not saying it can't ever be done, but I believe it's still a very long way off.
Cheers, Al