Wow, that's a lot of damage from a 1-2mph crash.
I don't know how the adjusters handle situations where the repair bill is close to the car value. I think I read once somebody saying they took the money for the totalled car, bought it back from salvage for $100, and got it fixed much cheaper.
My repair bill only came out to about $3500 (ha ha, only, good thing I had insurance). I've never had a problem with my insurance company (State Farm) - have had two accidents including this one over the past twenty years plus three comprehensive claims - two windshield damage (one from a rock and one when I put a windsurfer mast through it by accident) and one from when someone keyed my door. In all cases I just call them, give them the info, and then take it to the shop for repair. A lot of body shops here are what State Farm calls "Service First" shops, they do the damage inspection and estimates as well as repair, and my Acura dealer's body shop is one of those, so I just dropped it off there.
In this case, since multiple cars were involved, they also sent out a separate claims adjuster to divvy up the repair costs on my car, but I wasn't involved in that. I also had to talk to three claims adjusters on the phone, but only one of the calls (the one to my adjuster) took more than a minute; the others, from the people who hit me from the back, just seemed to be courtesy calls saying they'd be picking up the bill for part of the damage (all three were State Farm). The only thing I have to pay a deductible, they even have the rental car company bill them directly.
That's why I don't switch to those "lower-cost" auto insurance companies, you don't find out how good your insurance really is until you have to use it.
Hmmm, the above sounds like a State Farm commercial... but it's true, I'm really happy with their service.