The law clearly states that you can bring your vehicle to the shop of your choice!
Insurance companies can RECOMMEND if you ask but they MUST recommend multiple facilities.
An insurance company telling you that you should or worse yet MUST bring it to one of their shops is in fact illegal! STEERING is outlawed in most other states as well as Arizona.
If you do not know where you want to bring your vehicle, visiting a couple shops to find people that you feel comfortable with and confident in is a great idea but collecting estimates is a waste of time.
Some shops write a low estimate to capture the job knowing that they will be supplementing your insurance company during the repair process.
And by the way, do you want the shop that can do the repairs the CHEAPEST fixing your car? I don’t!!