Really interesting question and responses, most of which I agree with. Things have changed over the years!
Bellars used to allow customer supplied parts (early/mid 2000's), I know because I did that a lot with the M3. It doesn't surprise me that many no longer support this. As above, if you have a good relationship with a not-too-big shop, they will often accept customer supplied parts... there are a few members here with shops that will.
Main reasons for not supporting this are discussed above in this thread but, let's be honest, the bottom line is they make no margin off customer supplied parts and, for better or worse, that's their choice.
I have had recent success requesting work at a shop and indicating (with links) what I could land the parts for and advising them, that if they could match that price, I'd get them to order the parts directly (basically from FCP or Spareto). The shop set up a trade account with the vendors, got the parts cheaper than I could and made a little margin, I had to wait a few weeks for the booking (for the parts to arrive - also a challenge with the NZ BMW network because they keep very little in country), but I paid the same as I would have buying the parts directly, the shop made a little margin and was happy with the (genuine or OEM) parts, and we all walked away happy with less money lining BMW NZ's greedy pockets.
This problem wouldn't exist of course if dealers didn't want to put a 100% margin (or more), on parts. This is not a problem unique to NZ but BMW NZ really takes the piss.