Are there any drawbacks to a hypothetical climate policy?- Carbon tax for reducing Income tax
Prominent economist Greg Mankiw has been a prominent advocate of the kind of change you describe (he invites people to join "The Pigou Club", named for Arthur Pigou who first proposed these kinds of corrective taxes).

You can find a nice, non-technical summary of his arguments here. In particular, Makiw deals with some of the weaknesses you identify above and argues that they shouldn't be too much cause for concern.

Wikipedia has an article that lists other prominent economists who have jooined the Pigou Club by publicly advocating for a shift towards carbon or similar taxes (including links to many articles where the issue is disccused. It is here.