You assume that it will require power (read: coercion & violence) in order to deal with climate change.
For a few hundred years we've had an ever-growing state in most places in the world, reaching levels of power undreamed of by rulers of the past. Yet climate problems persist with no sign of stopping. Relying on the current political order will not result in anything different. All nations exist in a state of anarchy with respect to one another.
So we're at a crossroads: do we empower global government to control the entire population, in order to address climate problems? Or do we admit that government cannot solve the problem and look to more imaginative -- and less violent -- solutions?
I for one don't expect that global government will work out quite like its proponents envision. Is anyone fit to be King of the Earth?