And w.r.t. size of the bureaucracy, not so much either. The size of actual government bureaucracy is quite insignificant compared to size of transfer payments in this case. Like 1% or less.
And this particular tax has fantastic property; since it will drive down carbon use, the amount of tax collected will go down over time, thus reducing it's drag on the economy.
Hardcore market fundamentalists, like myself, love carbon taxes.
I agree with your post, but I would note that this is not entirely true in the US. Benefits that such as SNAP and Medicaid that are only used by a vulnerable segment of the population have been a frequent target for clawbacks. Social Security and Medicare are much more resistant to politically-motivated clawbacks yet not resistant to meddling in general since they are not enjoyed equally.
A benefit that exists at the level of “everyone gets $N per month” would seem to be much more resistant to political meddling.
The US government has a debt problem. The Social Security fund has lent money to the US government. Why can't similar things happen for the carbon tax fund?
I'm saying that whichever way you slice it, it's still possible for this to be abused.