Arizona splits the question in two. A diminished value claim in Arizona works against the driver who hit you. Courts have said no to the same claim against your own insurer.
Courts Allow It Against the Driver at Fault
Arizona courts have held that the owner of a car hurt by a careless driver may get the repair cost plus proven lost market value. That line comes from Farmers Insurance v. R.B.L. Investment in 1983. Oliver v. Henry in 2011 said the same, with an allowance for any gap between the value before the damage and after repairs.
Both cases are summed up in the MWL law firm chart of all 50 states. Note the word proven. You need a written appraisal or similar proof, not a guess.
The Johnson Ruling and Your Own Policy
Johnson v. State Farm, from 1988, went the other way for first-party claims. The court held that an insured's loss is not the gap in market value before and after the crash. So your own collision coverage pays for the repair and stops there.
Pure Comparative Fault
In Arizona, sharing the blame never knocks out the claim on its own. Under Ariz. Rev. Stat. § 12-2505, the action is not barred. Your damages are cut in proportion to your share of fault.
Two Years, $15,000 and Small Claims
The clock is short. Ariz. Rev. Stat. § 12-542 gives two years after the claim arises to sue for injury to property. Many drivers spend months on repairs, so mark the date early.
The Arizona Department of Insurance and Financial Institutions lists the minimum limits as 25/50/15. The last number means $15,000 for damage to the property of others. When repairs and lost value top that, a bare policy will not cover it all.
Small claims court takes cases under $5,000, per the Arizona courts. If an insurer ignores you, file with the department's complaint page. Drivers near the border can compare California.