Tranqing animals is more complicated than people expect. The dosage is variable and dependent on the target's size, weight, sex, metabolism and so on. For some animals a full stomach or a prolonged fast can make all the difference to the appropriate dosage. Too little and it won't stay down, too much and you can kill it or cause other damage. Considering these are large vicious predators people tend to err on the safe side, which is not the safe side for the target.

Nor are lions loners, if you want to take away the cubs you'll probably end up needing to deal with most if not all of the pride, increasing the risk that it'll go wrong for one of the animals.

Which brings up the next problems. Growing up in the wild is dangerous and complicated. There's a reason many animals throw large and frequent litters. Young animals have a low survival rate but are easy to create. Grown animals are independent and carry valuable experience. In the case of social animals like lions, adults are also group care takers. Many animal parents will defend their young viciously, they won't however expend energy on lost causes. This is less known because it doesn't make for great tv but animals will let their own young die or even kill them if it's the best option they have. In times of prolonged scarcity many animals will allow their young to starve to death if it means the adults can live to try and produce a new generation next year.

Objectively speaking young animals are fairly worthless compared to healthy grown adults. Depending on their lifecycle most animals reproduce frequently and in decent numbers, albeit it often with a high mortality rate. It's the adults, not the young that are most valuable.

In that light tranqing groups of lions going through their natural lifecycle to attempt to rescue litters of cubs that will most likely never grow up to be wild animals is a terrible idea. It won't help wild lions. It won't help the world's captive lion population, which frankly doesn't need any help and it won't improve the future of the species in general. Baby animals are not born with the expectation that all of them or the majority of them will reach maturity. It wouldn't even be a desireable outcome in most cases.

Poaching is a terrible thing but broadly speaking there's a lot more going on that's threatening wildlife and the reasons aren't always simple and straight forward. Habitat fragmentation can cause species to become endangered while there's still a sizeable population simply because animals can't reach each other readily enough to keep a healthy gene pool for instance. South East Asia has several severely inbred tiger populations that can no longer hook up with other tiger populations to produce healthy generations for instance. The tigers are there, the tigers are alive but they're facing worse problems than poaching. (which they do admittedly face)

Oh and male lions taking over prides are not exactly a predictable event. Males compete all the time and unless you want to have someone keep an eye on pride leadership full time I don't see how you're going to be there for the transference in leadership anyway.