We don't have a carbon tax in the US and we don't have requirements for carbon sequestration systems. Yet, the coal industry is still contracting. Now you could remove the regulations that require limiting emissions of things like mercury and NOX and SOX and it would make coal cheaper. But people really don't like acid rain or mercury in their water. Coal is already phasing out and it's because natural gas is cheap and renewables are getting cheaper every year.

Why would we ever do that?

Remember that the untaxed price of coal isn't a real price for it. Without a tax the market does not take the externality of its environmental effect into an account.

Economically speaking, a high tax on coal/other fossil fuels is simply forcing the market to consider its full and actual price.

Where are these carbon taxes? The only one I was aware of was in Australia, but that got repealed.