>Prices will adjust all the way down the supply chain
Hitting the poorest most, since rise in energy prices has a cumulative effect on everyday spending. Also "adjustments" can very easily lead to shocks if not done carefully. And don't forget, we are talking about it in a highly inflationary environment. To summarize: small mistakes in introducing such policy can easily lead to a sizable civil unrest.
>Use this huge income source as global helicopter money
So effectively you pay back money to people which they additionally spend due to the increased prices. In the best case scenario, additional spending and such UBI may equalize each other, but more realistically I think the former will be bigger than the latter. And I am not even touching the matter of exports becoming less competitive on global markets against countries which do not implement such policies. So I don't think that most people magically will be able to invest into green projects en masse.
Yes, eventually everything will stabilize and we will have an economy with properly taxed carbon externalities, but my point is that it's very easy to make mistakes on this path with very drastic consequences. And I would advice against magic hand-wavy thinking.