Summary: when using insurance, or not, you should focus on the MOST QUALIFIED roofer, not the cheapest one. There are a lot of good recommendations on this thread. I'd suggest using one.
First, I'm responding to your post but not "you". This is general "you". This topic comes up frequently.
Bear in mind that Many folks don't understand how insurance works. It's the project manager's job to explain that. If the roofing "dude" just scheduled materials and subs then you need a better project manager because there is far more to it than that. I handle everything from inspections, contracts, materials, educating homeowners on multiple brands and products, technology, managing crews, install day, material shortages, homeowner issues, billing, invoicing, adjuster meetings, supplements, all the way to litigation if a customer doesn't get what they are owed. If you didn't get upgraded shingles, hip and ridge, underlayment, manufacturer warranties etc, at a MINIMUM, they didn't do their job for you. When you cut out the roofing company, you also cut out your warranties, expose yourself to liability (I carry $2 Million) and you are at the mercy of the crew to fix issues if you can even get a hold of them. That crew is contracted by a roofing company, and when I have them busy for 6 days a week, guess where your roof issues falls on their priority list…probably 7 months from now. Why take that risk? You paid the same. Your insurance got a deal and you got shorted.
Folks can do it your way to be sure. The insurance company prefers it because it saves THEM $$$$$. You paid more for less. That's why they want you to get estimates, so they can get out of paying full price.
You paid your deductible and got a basic install instead of paying your deductible and getting a top grade install. That's fine if that's what makes you happy but I'm personally not interested in saving my carrier a penny. My homeowners pay a ton for their premiums and they want their pound of flesh in top grade materials when it's time to pay the piper.
When my truck got damaged, Geico wrote me a nifty check for $2,000 then they said they had "a guy". That "guy" magically could do the work for less than 2,000. Guess what…I don't want some "guy" to work on my Ford truck for pennies on the dollar. It goes to mother Ford and their estimate was nearly DOUBLE at $3800. It costs me the same $500 whether it's done cheaply and poorly, or expensive and nice. Ford made it look brand new and insurance ate every stinking penny of it. I hope Ford made a killing. I hope they overcharged Geico. Either way, I don't care, my truck looks awesome.
Treat your roof the same way. It's about the most important part of your home.