A carbon tax might've worked if implemented a couple of decades ago, when it could be gradually increased over time, and giving industries time to adapt. It is meant to be a gentle way for the government to change behavior.
But the scale of emissions reductions required now -- at least 10% per year [1] -- would mean that the price of carbon would have to immediately be cripplingly high. Obviously, that's bad for anyone who isn't rich. And there's no appetite for high taxes.
The point being, if the government is going to intervene to the degree that the climate crisis requires, then the government might as well directly shut down industries and institute regulations on behavior, instead of indirectly through carbon taxes. As we've been reminded of recently, the wealthy always find loopholes around paying their fair share of taxes.
[1] https://www.showyourbudgets.org/?country=united_states_of_am... And even this budget is likely conservative, as committed warming is a topic of debate.