OK, got it.Opposite. We filed a claim. They requested photos of the damage. They credited the credit card for the purchase price of the glasses. My wife then chose to re-purchase the glasses as she wanted a new pair, free from damage. There is no stipulation or requirement that you must purchase a new product with the claimed credit.
If we apply it here (which his American Express card covers up to $1,000 in damage). He can submit a claim. The device was $1199+. Amex will request photos of the damage and then decide to immediately cut him a credit for up to $1,000. He can then use said credit to repair his phone, if he so chooses.
Just one little quibble, and perhaps it is down to semantics, IDK. You state OP can the use said credit to repair his phone. But if Apple determines the damage is cosmetic, they will not repair the phone. So, OP would have to buy a new phone.
I'm not questioning that Amex or any other CC card will extend credit or reimburse. But this requires Apple to play along. Otherwise, OP would just have to buy new (or used) or take the phone to a repair shop.
But the iPhone 15 being brand new I can't imagine taking it to a repair shop.