A garage doesn't normally start repairs until the insurance company has assessed and agreed to what is to be replaced or repaired.They,the companies,have a limited number of assessors,who travel many miles to check many vehicles.unfortunately all this takes time.Again the garage usually only order parts after the vehicle has been assessed,they dont want to be left with parts which the company hasn't agreed to.
An accident can cause more damage than is obvious, until this is established no insurance company will risk a vehicle being used on the road until it has been assessed.
[ I have seen a case where the damage was superficial and after assessment the vehicle was allowed to be used until the body parts were received.]