A second faulty assumption is that a totalitarian regime would in fact protect the environment. Even if it we're put into place for that purpose, who watches the watchers? China is a good example... Nominally communist until the elite there gave up on communism and decided to get rich. A generation or two can change a lot.
True. I think the thing that a lot of the do-gooder types who wish for totalitarian government to solve some problem or other don't realize is the sort of people that kind of power attracts. Even if the people put in charge at first are the most wonderful, benevolent people the world has ever seen, it won't stay that way for long. Such people are just not ruthless and determined enough to stay in power in such a system for long. Somebody who cares for nothing but their own power will eventually find a way to bump off whoever's in charge and take control. Just the existence of those power structures are irresistible to such people.
It's kinda like the old regex quote - You have what you think is a serious problem, and you want to use a totalitarian government to solve it? Soon, you will have 2 problems - the original problem is still there, because nobody in charge really cared about it in the first place, only now you will be throw in the Gulag for daring to question what your new totalitarian leaders are doing.
I think China shows us that a totalitarian regime can in many cases be worse for the environment than even the most unrestrained laissez-faire capitalism. That's because totalitarian regimes will apply forcing functions to things like industrial activity and will make wasteful malinvestments for political purposes at scales far beyond the froth you see in market economies. Google China's ghost cities.