Yes.

> Hence taxing externalities and using the revenue for the common good corrects for that

That's the argument for Pigovian taxes and subsidies. The typical “free market” counterargument is that the government taxing and spending for the common good to correct that:

(1) violates consent and does not take into account whether and how much the individual “beneficiaries” would be willing to pay when taxing the public and spending for Pigovian subsidies,

(2) does not compensate for lack of consent or compensate the individuals harmed what they would be willing to accept to consent to the inflicted harms when collecting and spending pigovian taxes.

And, therefore, that the correct policy is for individuals who would benefit to subsidize third party action in place of Pigovian subsidies, and seek individual remedy, e.g. via the courts, for unconsented negative externalities.

> Hence it is free market.

That it compensates for what sone people see as a problem in unregulated markets doesn’t make it “free market”.