As soon as I read animals shot are not being replaced I thought of poaching. Unless the 'safari clients' are culling large numbers there is little chance of sensible safari trophy hunt numbers causing problems to herds. However not the same for native poaching. On a safari there are few days where evidence of poaching is usually not encountered.

Also hunting safaris get in the way of poaching activities. One reason local authorities often want hunting safaris eliminated. Eg why safari hunting in Kenya was banned.

Another angle is the "payoffs" from greenie organisations/NGOs etc whom want hunting removed, and their local stooges. Just another possible explanation.