Policies like the Carbon Tax are regressive - they hit all consumers equally, so in relative terms hit poorer people hardest.
It is very difficult to correctly measure something’s “social cost” accurately or proportionately - for example, with food, would you measure the carbon emitted from fertilising it, from harvesting it, from transporting it, from maintaining the land?
On an international level, there is a material advantage in not introducing price controls. If you are the only country imposing price controls, your goods will be less competitive.
Profits made by green businesses will still go into expansion and accumulation on a finite planet; all of which will use space, resources and labour. Solving the climate crisis will mean challenging the motive for profit and growth.