We do not give estimates to customers with totalled vehicles. Customers most times don't realize that the total loss threshold varies among insurance companies, and the type of car. A misconception is that "total loss" means the estimate is at or above 100% of the value of the car. Some companies put the threshold as low as 65%, most are at 80%. Too many times when a car is totalled and I (rarely, it's officially out of my hands at that point) verbally tell the customer what the estimate amounts to, they think that is the value of their car. Putting a value on a totalled car is not the shop's job, it is the insurance company's job. All I do is report the damage to the insurance company, and they make the decision, after running some numbers, on whether the car is economically repairable. They tell me what they want to do, and all I am able to do at that point is tell the customer "you will hear from your insurance company".
One of our insurance companies asks us to make 3 calls for salvage parts and 2 calls for aftermarket parts, even on a car that has 5 miles on it. Other companies aren't so anal about it, but I do call for any other company's customers if the car is a few years old. And we don't put junk on aything, it has to be in good shape. I choose our 3 biggest salvage yards that we do business with. They have locators to find parts at other yards all over the country. But it is not a perfect system. There are a lot of junkyards out there.
We have fixed cars that should have been totalled for elderly folks who have an older car in good condition, because the customer doesn't want the expense or unfamiliarity of a new car, and because the car wouldn't bring much in salvage for the insurance company. But the vast majority of the time, the insurance company acts as a business based on numbers, with not much room for emotionality.
As for your bumper cover, Brian, most times I try to engage the customer and ask them about prior damage. That bumper cover was cut only because of the scuff in the textured area, which made it unrepairable. The estimator was trying to write a complete estimate when he saw that, but... he should have had you there while he wrote it so you could point out things like the fact that was a prior spot of damage.