It’s probably too late for a tax-only solution. Either the tax is too low to have the necessary effect, or people will overthrow the government who instated it. The change we need has become quite drastic.
That would have been a great strategy about thirty years ago. Now we can’t really afford a measure that only really starts working a couple of years in the future. We already know pretty well what needs to be done, we don’t need the market to figure it out for us.
The rest will happen without extra nudging just because doing it "the wrong way" will be too expensive.
By feeding carbon tax money into carbon extraction we can eventually start reducing amount of carbon in atmosphere.