I am going to question you on why most of the Earths large animal species have died out, when they should be thriving. and I am pretty sure Humans would have tried to preserve them.
Climactic chaos, mostly. I am of the view that the mass extinction event we're living through has not been caused by humans (though we've certainly exacerbated things), but rather by rapid, punishing fluctuations in climate brought on by the present ice age. This will continue for some time after the human departure from Earth, and it's inevitable that larger, more specialised species will be the ones least able to cope with this. Even if humans retain DNA blueprints for these species, they're extinct on Earth and their niches have been taken over by new species.