So it turns out there's a serious argument (HT and text summary: Bob Murphy) that a "green tax shift" may be welfare-worsening rather than welfare-improving. (The green tax shift is where you cut taxes on labor and capital while raising them on environmental "bads" like CO2 emission.)
Huh? How can a tax shift off of bads and onto goods be welfare worsening? It seems the argument is somewhat subtle; even Bob Murphy dismisses clarification requests in the comments, pleading that "it’s hard to point to 'what’s driving the result' except to say, 'Adding the carbon tax drove the result.'"
Well, it's actually not that hard, but the standard expositions don't make it explicit. After reading another of Murphy's articles, it finally clicked for me, although the better explanations still hid the true mechanism in unstated assumptions. Here's how I explained it in the comments (cleaned up a bit and sourced).
I think I have an explanation that conveys the intuition.
Insight 1: the harm of a tax is more-than-proportional to its magnitude. (This is the assumption that the writing on this seems to assume and which I wish was made explicit here and in your article.) Mankiw gives the rule of thumb that the deadweight loss of a tax increases with the square of the tax rate. Thus why you want to raise a given amount of revenue from as “broad a base” as possible -- to lower the rate each tax has to be.
Insight 2 (most important): Because of the above, each increase in tax above the Pigovian level is more harmful than the same increase from zero.
Insight 3: Taxes on anything chase back to their original land/labor/capital factors. So a carbon tax amounts to a tax on land, labor, and capital, divided up per their relative supply/demand curve elasticities (slopes).
Given the above, the intuition becomes a lot clearer: a tax on carbon is like an income tax (with different levels for different kinds of income). Levied at the Pigovian rate, it merely cancels out the carbon harms. But if you have an additional (direct) income tax, you get a disproportionate harm for each (potentially) taxed dollar above the Pigovian level (compare to taxing from the first dollar) — *that* is the tax interaction effect.
Furthermore, since the “green tax trade” tries to raise the same revenue on a smaller base (i.e. only those income sources touching carbon), the tax rates have to be much higher than they would be if they were on all income. This then causes major welfare-harming changes in behavior, far out of proportion to the assumed harms from carbon.
Problem solved, right?
Well, no; Bob insists that Insight 1 is irrelevant to the argument. But I don't see how this can be; you can only get the bad "tax interaction effects" if the tax's harms are more-than-proportional to ("superlinear in") the tax rate.
If it's merely proportional, the taxes don't "interact" at all -- raising taxes by 1 percentage point (on any kind of income) does just as much additional harm, regardless of whether it's on top of a 6% existing tax, or a zero. But when it's more than proportional, then that extra point of tax is (badly) "interacting" with whatever other taxes got it to that level. This is the key insight: that having income taxes in addition to the (implicit income tax resulting from a) carbon tax means those taxes are doing more harm than they otherwise would.
Likewise, if the harm (deadweight loss) of a tax were less than proportional to (sublinear in) the rate, then they would interact in the opposite way. It would make sense to have as few distinct taxes as possible, on a small a base as possible, with as high a rate as possible -- because in that case, each additional increase in the tax rate hurts less than the previous. (Obviously, we don't live in that world!)
I note, with some irony, that this point ultimately reduces to the reasoning behind standard mainstream economist's tax advice to "lower the rates, broaden the base", a mentality Bob actually criticized in another context...