this is not always true.
many idols of gods in less famous and out of the way hindu temples in india were stolen and sold off to collectors in the west. these idols were there in the community forever and cared for, when they were stolen, the community simply accepted the loss because they didnt have the resources to chase it all up.
see this: https://www.newyorker.com/magazine/2007/05/07/the-idol-thief
from the article
Collectors often suggest that they are the custodians and preservers of antiquities that might otherwise suffer from neglect or mistreatment, but Ghiya described the callous mechanics that are sometimes required to smuggle a statue from one country to another. He recalled a squat stone Vahara—a depiction of Vishnu in his incarnation as a boar—that stood in the village of Attru, in southeast Rajasthan. The boar weighed more than a thousand pounds and its legs and torso were covered in a magnificent phalanx of tiny, intricately carved figurines. Ghiya’s thieves stole the statue in the late nineteen-eighties, lacing a chain through the boar’s open mouth and yanking it from its stone pedestal, shearing off its lower jaw and breaking its legs in the process. The piece was eventually sold to a private collector in Zurich.