U.S. airlines pay a depreciated value - not replacement value. They will also pay zero for any items one shouldn't have checked, anyway, and the list is long:

antiques, artifacts, artwork, books and documents, china, computers and other electronic equipment, computer software, fragile items (including child/infant restraint devices such as strollers and car seats), eyeglasses, prescription sunglasses, non-prescription sunglasses and all other eyewear and eye/vision devices whether lenses are glass, plastic, or some other material, furs, heirlooms, items carried in the passenger compartment of the aircraft, liquids, medicines, money, orthotics, surgical supports, perishable items, photographic, video and optical equipment, precious metals, stones or jewelry, securities and negotiable papers, silverware, samples, unique or irreplaceable items or any other similar valuable items

If one thought the Montreal Convention limit is $3000, so AA will just hand you a check, that thinking is flawed.