You can have sheep spend the summer there. GMO wheat fields, not.

Methane and waste, well, maybe. It's not clear to me that there can be enough sheep there that the waste is a problem. I've never even tried to quantify the methane.

Energy and water aren't issues. The energy to gather the sheep in the autumn is a rounding error, and how would you water such an area anyway?

You can't grow crops on that. No one's watering it. The only energy use is rounding all the sheep back up.

As for methane... well it's not the land that makes that, but the sheep. You're going to have that problem as long as you're rearing ruminants to eat. There's a lot of research being done on that - it's possible we'll be able to engineer low-methane sheep...

Just pushing things further, since I appreciate your insight, in terms of nature (as opposed to feeding humans), wouldn't a more natural ecosystem be preferred? Might it better help protect against extinctions and such?