Unfortunately, in practice these arguments don't hold up. For one, some governments are more interested in how much a dead lion can bring them than in establishing sustainable hunting limits. For example, there are around 20,000 to 35,000 wild lions left in Africa, depending on whom you ask, and big game hunters legally kill around 600 each year. That's an annual population loss of 2 to 3 percent, which is entirely unsustainable, even if you don't add in deaths due to poaching and livestock protection.
And while nature likes to pick off the weakest members of a population, big game hunters target the largest, strongest members of a population. For lions, that means the male pride leader; for elephants, the oldest elephant with the biggest tusks. Killing these animals, who play a crucial role in their societies, puts the rest of their families at risk.