The problem with the externalities argument is that nobody really knows what they cost. A market solution would be based upon true supply and demand and agreement on price in buy / sell transactions. A tax representing the "externality" is just a politically made-up number. So it's sort of free market but not really.

> That is a free market solution.

No, it isn't. Taxes are not free market solutions. End of story. Taxes are government interference in the market; this isn't debatable, it's just a fact.

> And when the tax is directly addressing externalities that are normally not paid, it makes the market less distorted.

Agree, but that doesn't make the tax a free market solution. A free market solution would be a solution from the market, not a government imposed tax.