Problems when insuring a classic car with regular auto insurance:
The insurers will only recognize the trade in or market value of the vehicle (not your full appraisal or purchase price).
Special after market or hard to find items may not be replaceable or covered.
Claims are determined by an adjuster who is working for the insurance carrier (not you)
Your standard car insurance carrier may not cover a modified vehicle, or one that has been improved for performance or looks.
Some insurance carriers simply may not insure your car if it's older than a certain year
The auto insurer may not give you the large discount for mileage you're entitled to, especially if you rarely drive the car.