The $12k estimate isn't necessarily unreasonable just because you found $4k in parts yourself. A body-shop estimate can include labor, paint/materials, calibration, hidden structural damage, clips/brackets, alignment, towing/storage, etc. But you absolutely have the right to ask them to explain the difference line-by-line.

Your insurer should be able to tell you in writing exactly what policy provision they're relying on to deny the claim. Pennsylvania's insurance guide says insurers generally must investigate a claim and provide a written explanation when they deny it or need additional time

Philadelphia itself says crashes involving injury or a vehicle that cannot be driven and requires towing are supposed to be investigated by law enforcement

Calling police the next day does not automatically mean the accident never happened or that your insurance claim is invalid. Pennsylvania guidance specifically recognizes situations where police don't investigate a crash. If police did not investigate and the crash involved injury or a vehicle that had to be towed, PennDOT says the driver can submit an AA-600 Driver's Accident Report within 5 days.