Of course stopping climate change will save in the long run. The critical question is who should spend the money now to save money later. That is the crux of the free rider problem.
I don’t like that we’re even talking about money in this context. Money is almost fake, it’s right there in the ‘fiat’ name, yet that’s all most people care about.
Money isn't fake, it's a useful abstraction for describing the allocation of goods and services. We could describe the cost of transitioning from fossil fuels in terms of labor hours spent, miles not traveled in an ICE vehicle, tons of lithium mined, etc. But money lets us collapse all of that down into one number that we can get our heads around and which is useful for figuring out things like how much we need to raise taxes
Just because it is not solid, does not mean it is not real.
As long as it has value to people - it is real.
Meaning, as long as you can use it to buy things.
And that is what people care about.
That stops the moment, people don't believe in the currency anymore. Then they will either use a different currency they do trust - or go back to trade little pieces of gold.
In this context money is just a unit of measurement. If we say that we need more of a particular kind of infrastructure and reduce a particular kind of activity, etc, then the discussion requires being able to say how much of those (many!) things and we can quantify all of those in terms of dollars.
It's a strawman to say that money is fake because no serious economist argues that money is "real". Of course it is fake. We use money because it's a useful way to organize society
My point is you need a society to use it and climate change will cause events which will make people question whether we still have one - which is enough for money to stop being useful. People in the west take a lot for granted.
Even in disaster scenarios like hurricanes, where everyone is going to do nearly everything they can regardless of cost to survive, money is still used in practice and in discussions, evaluations, planning. In a practical sense money is real not fake, because what money is used for, limited resources, is real not fake.