This might also have the desired effect. Increasing the price of a product would make it less desirable. Unless those companies have enough power to lobby and keep adjusting regulations in their favor (hidden subsidies, additional roadblocks for competitors, etc.).
Either way we're spending more because free work doesn't come from nowhere. Mass carbon cleaning will drive the price up on everything.
Damage from climate change won't exactly be free either. We're already starting to pay those costs.