It seems incorrect to conclude the public wants to reduce X when it taxes X.
The minimally logical conclusion (to me) is the public doesn’t want to pay for the externalities of X. Taxing X—assuming the tax levied is an appropriate amount to cover the externalities of X—makes actor Y who is doing X pay for X and its externalities, alleviating the burden on the public while avoiding taking an actual stand and/or engaging an effort to reduce X. Y does X? Y pays for it, not the public.
How much taxes on X adds to public revenue is mostly irrelevant, so long as it is enough to cover the costs of dealing with X without shifting that burden onto the general public via other taxes. If the revenue from X is enough to cover the costs of X’s externalities and also pays for wages and/or other public needs, that’s a net win for the public. You likely won’t see a city starting up a campaign to increase undesirable thing X just because it’d increase revenues.
Now, if the public really wants to reduce X by means of taxing X, it will likely choose to levy heavy, punitive taxes on X as doing X increases/continues, hoping to make it financially painful to those doing X to have to pay for X—for example, look at cigarette taxes. That can only go so far, though, before you encounter those for whom the added punitive tax is not a sufficient deterrent. Then it’s either a choice between more increases to get X to zero, or some other type of concerted public or legal effort to curtail X.
The act of taxing X isn’t enough of a signal to conclude the public is using the tax as a reduction effort. But it’s certainly a signal that the public doesn’t want to pay for X via standard revenues—and the public absolutely should not bear the burden for the negative externalities of any X. There’s no doubt a built-in hope that, assuming the costs of X’s externalities are known, taxing Y to pay for X will encourage reduction because—especially if Y is a company—Y wants to keep their expenses low, and really doesn’t want to pay for X. A city levying such taxes, assuming it is even moderately well-managed, will hope to see that the tax revenue for X will hit zero in tandem with X itself hitting zero—the success state[0].
[0]: I’m going to ignore the real-world chance that revenues from X get allocated to previously non-existing programs that then need to find a new source of revenue—but that’s a different problem.
The example I was thinking of is [1] - "Revenue-hungry cities mess with traffic lights to write more tickets [...] cities and towns shortening yellow lights spike the number of tickets, and thereby increase revenue. The profits come at a social cost, as shorter yellow light times have been associated with an increase in car accidents."
In that case, X=car accidents - any public red-light-camera advocacy will say they reduce X.
Of course, you're right to say that a tax on X doesn't prove people dislike X - a tax on income doesn't mean citizens hate income. You could even argue a tax on alcohol means citizens like alcohol too much! But a subset of taxes, such as fines and some sin taxes, are presented in the public discourse as about reducing X rather than making money.
I’d agree that some taxes are presented in public discourse as at least partially being about reducing some X—though fines shouldn’t be lumped in with taxes. Fines are worth considering as a different thing with their own reasoning and goals that often make them distinct from taxes—particularly because fines are punitive and come after known legislated/regulated behavior has occurred.
The minimally logical conclusion (to me) is the public doesn’t want to pay for the externalities of X. Taxing X—assuming the tax levied is an appropriate amount to cover the externalities of X—makes actor Y who is doing X pay for X and its externalities, alleviating the burden on the public while avoiding taking an actual stand and/or engaging an effort to reduce X. Y does X? Y pays for it, not the public.
How much taxes on X adds to public revenue is mostly irrelevant, so long as it is enough to cover the costs of dealing with X without shifting that burden onto the general public via other taxes. If the revenue from X is enough to cover the costs of X’s externalities and also pays for wages and/or other public needs, that’s a net win for the public. You likely won’t see a city starting up a campaign to increase undesirable thing X just because it’d increase revenues.
Now, if the public really wants to reduce X by means of taxing X, it will likely choose to levy heavy, punitive taxes on X as doing X increases/continues, hoping to make it financially painful to those doing X to have to pay for X—for example, look at cigarette taxes. That can only go so far, though, before you encounter those for whom the added punitive tax is not a sufficient deterrent. Then it’s either a choice between more increases to get X to zero, or some other type of concerted public or legal effort to curtail X.
The act of taxing X isn’t enough of a signal to conclude the public is using the tax as a reduction effort. But it’s certainly a signal that the public doesn’t want to pay for X via standard revenues—and the public absolutely should not bear the burden for the negative externalities of any X. There’s no doubt a built-in hope that, assuming the costs of X’s externalities are known, taxing Y to pay for X will encourage reduction because—especially if Y is a company—Y wants to keep their expenses low, and really doesn’t want to pay for X. A city levying such taxes, assuming it is even moderately well-managed, will hope to see that the tax revenue for X will hit zero in tandem with X itself hitting zero—the success state[0].
[0]: I’m going to ignore the real-world chance that revenues from X get allocated to previously non-existing programs that then need to find a new source of revenue—but that’s a different problem.