Insurance is a very tricky thing with people.
On one side you have the person who hates to pay their monthly premiums because they think they will never have an accident or a loss. To them it is just another bill like paying your cell phone or electric bill. Just like your story above, these scenarios happen here & there but many times there are reasons. Your friend who fixed it probably "hooked you up" while the adjuster figured the worst case scenario, punched repair cost & times into his laptop (the rocket science you were referring to) and came up with a number. Body shops charge a lot of money per hour to repair cars and have a guideline they need to follow, especially if the body shop that is being used is a licensed shop that has to repair the vehicle as if new because maybe it is a lease and will be resold later. They are not going to slap some bondo on the car, sand it, spray paint it and send it on its way. So to many, insurance companies do have that "stereotype" of taking your money and giving you back little when you need it.
On the other hand you have the person who very much believes in having the protection there to replace their car or home in the event they have a loss. Or more important, when a spouse dies and leaves a family with a ton of bills, a mortgage on a house to pay, a 2 girls that will need to go to college one day... I have personally hand delivered only 3 of these checks while an Allstate Agent and I can't tell you how important that Life Insurance policy was to that family. It does not replace the person that died but it does replace the financial burden that may have been left behind. It allows those kids to go to college, it allows that spouse to keep his or her house, it allows that family to retain the lifestyle they had before the loss. If you ask me, insurance is sometimes one of the most important things you pay for during your life. We replace the most valuable things you lose. Some of those things you can not even put a price on... So to them insurance is very valuable.
I am an agent that has many relationships with many of my customers. To some I am as important as their doctor or accountant as I the person they will come to when they have that devastating loss. It is important to them to have a face with the money they pay for insurance. They know if they call me that I am there and will handle their loss. I am also involved with a few community organizations and represent Allstate in them. It is what separates me from your on-line, faceless companies that advertise a lot here in the states.
Insurance is not the most exciting or fun job in the world but it does pay the bills, allows me to be my own boss and most important, it allows me to help families and people recover when they lose their car, home or loved one...
Hopefully you have "lived & learned" a little from my post and seen a different side of where your money goes

Dave