Is there a demand for public goods? Yes. Are there suppliers of public goods? Yes...government organizations supply public goods. All that is needed to turn the public sector into a free-market is to give taxpayers the freedom to choose which government organizations they give their taxes to.
If I have to pay taxes anyways...and I value environmental protection...if I perceive that the environment is in need of protection...then why would I hesitate giving my taxes to the EPA?