I don't think this is a matter of principle; I think it becomes a matter of practical politics.
Carbon taxes are good. To get them in place, whatever it takes.... If that means reducing other taxes so that the carbon taxes are revenue neutral, that's pragmatic politics. If it means devoting the revenues to environmental causes, people tend to see that connection. Although the theorists say there's no necessary connection between the revenues you raise from a carbon tax and the expenditures you should devote to the environment, if the public perceives that and is prepared to support the tax more on that basis, then I think it makes sense.