To keep the income tax for just the upper bracket would also restore Congress' original intention when it enacted the tax in 1913. The goal then was partly fairness—the income tax balanced off the rest of the federal revenue system, which consisted of tariffs and excise taxes that fall heavily on those of modest means. But more, it was to exact a just return from those who accrue unearned gains from land and natural resources. (I explain all this in greater detail here.) The waste of these is a big contributor to climate change, so tax justice turns out to be environmental sanity as well.
Let's put this all together. Based on what Alaska does already, we would have taxes on sources of carbon in the atmosphere, the elimination of the income tax for the vast majority of Americans, and dividends for all. To this we would add limits on the emissions of carbon. It is understandable that Alaska wouldn't have such limits, because it's something better done at the national (or, better still, international) level.
The package isn't perfect, but nothing is. It will require some adjustments in details, but then these big-picture proposals usually do. We could even give it a catchy name: Let's call it a "climate dividend." It sounds a lot more promising than something called "cap and trade." To this extent at least, the (soon-to-be) former Alaska governor deserves some praise. She's given us a better start than most people seem to realize, including herself.