It is false economy to avoid claiming damage to your vehicle because they may raise your rates. If this is your first claim in 2 or 3 years, and you don't have more than one ticket in the past 5 years, they probably won't raise your rates.
If you had other claims or other tickets, they might raise your rates but even that is not too dramatic in most cases.
When my wife wrecked my first Sport Trac and damaged two other vehicles (one was totaled for $7000). I had over $2800 damage to my Sport Trac, and 6 people went to the hospital in ambulances ($750 each), thankfully there were no serious injuries and everyone was treated and released. My rates only went up $35 for a 6 month policy (or $70 per year)
I have since left State Farm after over 25 years and now have GEICO. I have more coverage with GEICO and it's much cheaper (about $400 per year cheaper). That includes 3 tickets and three claims in the past 4 years and full coverage on my 2008 Mercedes.
I had State Farm for many years without an accident or claim and found I was overpaying for my insurance. The insurance agent was worthless since he did not process claims or try to save me any money and he gets a commission from my premium. Now I get my insurance online, and don't have to worry about paying a salesman/agents commission. Now I pay for the insurance and I expect them to pay, which they do. If they start jacking up the rate, I will go to another insurance company that has cheaper rates.
Insurance companies will not be loyal to their customers and so I don't feel obligated to be loyal to them.
...Rich