Plausibly true - but the "do such programs statistically reduce firearm crimes?" analysis is incomplete. Humans and their societies are not numbers.
By the standards of city budgets, firearm buyback programs are not all that expensive. For people with a less-than-wanted firearm in the house, they can be an escape hatch from fear and anxiety. They broadcast some polite and restrained anti-gun messages (not everyone wants guns around, people should have the choice). They can provide healthy, positive citizen <==> police social interactions in places where those are far too rare. And (local politics willing) they're good, symbolic gateways to more substantial and lasting work toward addressing crime and social problems in a city.
By the standards of city budgets, firearm buyback programs are not all that expensive. For people with a less-than-wanted firearm in the house, they can be an escape hatch from fear and anxiety. They broadcast some polite and restrained anti-gun messages (not everyone wants guns around, people should have the choice). They can provide healthy, positive citizen <==> police social interactions in places where those are far too rare. And (local politics willing) they're good, symbolic gateways to more substantial and lasting work toward addressing crime and social problems in a city.