It's fundamentally misguided and it's not a solution. Between elephant extinction and elephant suffering, I will go with extinction every time.
Elephants are important for the ecosystem, IIRC something like 70% of all species in certain areas rely on them. If you remove them from the ecosystem by domesticating them, you are doing a damaging the ecosystem in multiple way.
No, elephants can't be contained on a farm. They are meant to roam whereby they disseminate seed of certain plants that rely on them to be disseminated.
Is that enough of a reason? Libertarianism is the answer only when you care about simple answers, not about working answers.
I'm not sure why you think this is an either/or proposition. I mean, I accept that farming elephants isn't practical for a lot of reasons, but no one's talking about putting every living elephant on a farm.
I don't think you should be. I'm glad people are thinking up solutions, even if they turn out not to work.
It isn't an unreasonable naive idea. After all, domestication (turning them into symbiotes) has helped some species enormously. Others that could not be domesticated (e.g. whales) have survived only thanks to technological change. Even "wild" animals like deer and trout survive through a symbiotic relationship.
Yes, I understand it doesn't make sense for elephants in particular, and of course domesticating some animals usually spells doom for others. So I understand there's an argument to be made that domestication is inherently bad -- one I disagree with but there's a legit case to be made. But I'm glad people actually care.