I definitely think this is backwards. its the humans that are less likely to overhunt the animals that they evolved alongside. If the animals are part of your culture/religion/ecosystem you’re not going to wantonly destroy them. But as humans spread, the animals may not have meant as much to them culturally, or they didn’t know how to not overexploit them. Like the first people in north america were likely a key factor in the loss of megafauna, but then became stewards of many existing megafauna/ecosystems as their culture adapted and they became more grounded in place