In a wreck, should I go to the repair shop my insurance recommends?

Regarding whether to go with the shops the insurers recommend, there is only one reason they recommend them: To cut costs. They are notorious for cutting corners on repairs.

The BAR (Bureau of Automobile Repair) has a program where they check into repairs, upon request, and they have found instances where, for example, another $12,000 of repairs which were NOT performed were necessary just to make the car safe.

For some of the shenanigans that go on in shops recommended / affiliated with insurers, check out this article:

https://oag.ca.gov/news/press-releases/attorney-general-lockyer-files-50-million-consumer-protection-lawsuit-car-repair

The practices may be better now, but the enforcement is more lax.

You should consider rejecting the shop the insurer recommended and find a small, local, family-owned shop that has a very high customer satisfaction rating and good reputation. Try YELP!