This is tripe.
Fundementally, the long term preservation of profits neccesitate environmental sustainability, so if your assertion that greed is the driving factor is true, capitalism will also be a driving force in the long term fight against climate change.
https://www.adamsmith.org/research/its-easy-being-green - the link at the top for the full paper, it's a good read
I might get time to read the whole paper at some point but based on the summary I don't see how you get to a conclusion that capitalism is the solution to climate change.
First let's start with long-term preservation of profits. Yes, technically you are right, but very few if any companies at all are looking so long term in regards to sustainability. We are talking decades, not years. Climate change is not going to suddenly create a mass extinction event like in 'The Day after Tomorrow'. Yes companies are slowly becoming greener, but not to the extent needed and only so long as profit margins aren't lost. It's why environmentally friendly initiatives and products like electric cars have taken so long to develop, because companies only do it when it is financially viable.
Now in the summary it starts with innovation, yes capitalism and investment does drive innovation, especially cost reduction. However, this links to the next point, which is that the market system leads to good stewardship. (Bullshit) as the article I linked showed, companies exploit until resources dry up then move on. Look at the amazon, despite a few attempts, more and more trees are lost every year and not replaced. In the long term this will be a disaster and destroy the ecosystem of the rainforest if it continues. That is not good stewardship. On top it says it leads to producing more and wasting less. Yes you waste less, but overall production doesn't lower. If you save on resources, you don't leave those resources there, you just use them to make more. This argument is flawed, because it implies that resources are not used, when they will be used, just for in something else. As for the protection of land and resources, I imagine they go into more detail in the main paper, but any protection is only to allow exploitation later. The implication that companies protect land and resources to preserve them is nonsense.
Now the point about socialism failing. This is one of the most pathetic arguments relating to capitalism. "Well socialism and communism don't work." It's a flawed argument and the same one the conservatives have been using. It's the argument of, "well here is an example of something worse, so ours must be good." Just because you are not the worst, doesn't make you good. The implication that capitalism must be the solution because other models and systems have failed previously is ridiculous. it also shuts down any conversation for trying to learn from the past and develop different newer systems that could be better.
Now as to the 3 main points. Well yes nuclear energy could help relieve the reliance on fossil fuels. As
@The_Blindside said though it ignores the issue of nuclear waste over the long term. The paper assumes that nuclear energy is a magic bullet and there is no evidence to say it definitely is. On top while Britain itself might be safe for reactors. Japan has shown there are places that aren't safe and climate change is not a UK issue, but a global issue. The world needs to develop safe, renewable energy sources, which this paper doesn't answer. Next carbon tax. Well that's just taxing coal to make it less financially viable. Not sure how that is the market being good for the environment because the proposal is essentially using taxation as a way of regulating the industry and that is actually more socialism than capitalism, because if it was capitalism then you wouldn't have any regulations at all. So number 2 for me is not a benefit of a market economy as it is about central government restricting one area of the market intentionally, not letting it develop independently through the market which is what this paper is trying to suggest should happen. Finally clean free trade. Again I'd probably need to read in detail to find the nuance of their argument, but it seems strange that the solution to high carbon footprints is to import rather than develop methods to lower the carbon footprint of products made in the UK. This is especially confusing when apparently "The market system naturally drives towards good environmental stewardship — through the profit mechanism that rewards innovation that produces more using less resources and waste". Surely if this were the case we wouldn't have to rely on importing because while importing in some circumstance may have a lower carbon footprint, transportation still does have a high carbon footprint and so is not a long term solution, especially not until transportation stops using fossil fuels. Further once restrictions are removed then production would probably be scaled up and that would likely increase the carbon footprint making the whole situation redundant.
Also nowhere does this paper mention the issue of overpopulation which is a huge issue. A capitalist, market economy that caters to consumers demands can only react one way to this. More.
Basically none of this convinces me that capitalism and a market economy is good for solving climate change. Yes it can help and maybe even have some impact, but ultimately, it can't solve the problem, because it is the problem. Capitalism is the exploitation of resources for profit. While companies can get more efficient at exploiting they cannot stop and that's the point. At some point humans will need to choose to stop exploiting certain resources in order to preserve the planet and needing to make a profit will always be counter intuitive to that.