I've had a similar experience recently. My driver side mirror was broken in an incident where the other driver failed to stop. I reported it to the police who are interested in speaking to the other driver in case they were uninsured and the local authority are checking CCTV (if it's you and you're reading, thanks).
Anyway, I initially didn't want to claim insurance for all the same reasons and got some prices from my local (non i) dealer as follows (all include vat but not labour):
Outer shell £48
Paint on above £72
Bottom bit with LED indicator repeater £52
Whole assembly minus glass £700ish
I decided to go down the insurance route.
Problems I've had so far:
Non i dealer can't do it, as every i3 or i8 worked on has to have a PUMA case opened with BMW. Same with other new flagship cars, it enables BMW AG to collate all issues quickly and act accordingly rather than wait a year or two for warranty stats to shake out.
I didn't want a 140 mile round trip to i dealer to change a mirror so local BMW bodyshop had to seek permission from area manager to deal with car, no problem as it's not HV related, but PUMA case still opened and car still has to be isolated, and it still took a couple of days to get this done.
Extra expense incurred - bodyshop is replacing everything to avoid future issues, this involves removal and replacement of door skin, although they've told me this is a simple "pop off" job, with new clips when putting back on.
All in all, it's over a grand and insurance is covering it, but for you £2100 sounds quite high given that my local BMW bodyshop have indicated it's a "while you wait" job now the paint has been done, only a few hours of labour.
Car going in this week hopefully.