You make a fair point that global climate change is of course a global phenomenon and that it must be tackled by at least a fairly substantial portion of global emitters, if not the whole world. That does raise very important challenges for coordination of policy, and yes, if any single nation acts independently, it will fail to deliver much in the way of measurable climate benefits.
However, I have addressed this issue in my paper, and discuss it my series when considering the political economy constraints on carbon pricing in Part 1. These constraints already internalize this dynamic. That is, since nations and individuals are concerned about the "collective action" nature of climate change (see Part 1), they will discount their willingness to pay for mitigation relative to the societally optimal. That concept is a central premise of my series, and your comments have not raised any additional points that I felt needed addressed on that matter.
Instead, I have focused on proposing a policy strategy that can succeed within the political economy constraints of each relevant national or subnational actor. If the policy framework as a whole can succeed in each nation, then it can succeed globally. In my view, climate solutions will emerge bottoms-up, nation-by-nation, not via a global top-down treaty, so I focus on the national-level policies here. You can disagree and prefer a global solution -- or a liassez-faire "free market" solution -- but that doesn't mean I need to change the entire focus of my series to accomodate your comments.
Regarding your "free market" alternative, it makes no sense to me. You talk about "removing barriers" to the free market functioning, but there is no clear evidence that the obstacle to tackling climate change is a lack of free markets. Rather, you must understand that "free markets" do nothing to consider externalities, of which climate change is the most complicated and challenging externality of modern times. You argue that regulatory barriers have prevented nuclear from scaling sufficiently by adding to its cost and regulatory risk. That may be so, but removing those barriers and shifting to a "free market" absent any regulation seems like a rather foolhardy way to handle a technology with as much inherent risk as nuclear energy (and I say that as a strong proponent of nuclear power), just as it would make little sense to have no regulations for airline safety, vehicle crash tests, or any of a wide set of regulations necessary to check the tendency of "free markets" to ignore externalized risks. Neither to a believe that "free markets" acting on their own will deliver the level and pace of technology innovation needed to develop clean energy technologies cheaper than fossil fuels. The history of government involvement in just about every substantial innovation of the last 100 years (and more) would bely that point as well. So when I stopped engaging, it was because I have no idea how your proposal would help much of anything.