I am for, when several conditions are met. If the same species is released, it is OK. Especially, if the species itself is threatened, as you said. When it is a different species, preferably from the same genus, there should be a clear idea what was the ecological role of the extinct species, which needs to be replaced.
It can be tricky, because even closely related species can have different ecological requirements and roles. For example, introduced American mink in Europe is much more damaging to native waterfowl and water voles than native European mink. That Polynesian, black and brown rats introduced to islands have different effect on native fauna is also well known.
So I am for, for example, restoration of Bolson tortoises in Texas, Aldabra tortoise on Mauritius and Reunion, european bison, kulan and water buffalo in Europe, bison in Siberia, and possibly e.g. saiga and Przewalski horses in American prairies.
But otherwise, it gets tricky. The idea of living cheetah replacing extinct American cheetah comes from the fact that pronghorn run with higher speed and extreme endurance excessive to outrun any living American predator. The hypothesis is that it is an relict adaptation to escape American cheetah, no longer useful. However, living cheetah has much higher sprint and absolutely no endurance. So living cheetahs clearly are a bad replacement of the American cheetah. And pronghorn are not over-breeding, so there is no obvious need of an additional predator to regulate pronghorn population.