It's not nice that they are picking and choosing what parts to send to watchmakers who they have authorized to do repairs. And it's hard to see the justification, unless they are specifically concerned about the parts being used to repair vintage movements. I don't know why they would care TBH.
As an independent watchmaker, Omega doesn't dictate to me what I can and cannot repair, at least not directly. So I regularly service and repair a lot of Bienne only movements. The "Bienne only" is for actual service centers, and this is why for example the 321's were not done by STS in the UK, but whatever their sister company is (can't recall the name off the top of my head). STS as the official service center couldn't do them per Omega rules, even though it could actually be the same watchmakers in the same shop doing the work, just under a different name (not saying it was, but it could be). The whole thing is a little convoluted to be honest.
The thing with 321 parts specifically, is that they still have some available to purchase, so I can still buy the pillar wheel (column wheel) for example, plus a number of others, but a lot of the key parts are discontinued, so things like pallet forks, escape wheels, and some train wheels, plus a lot of chronograph parts - the hammer spring is a well known discontinued part that some suppliers have actually had made in order to keep watches going.
If they didn't really want people working on these, why sell any of the parts? If you are going to sell some of the parts, why not sell them all? It doesn't make a lot of sense, but it is what it is...