The only thing that will make possible a shift to carbon neutral or low emission forms of energy is a shift in the mode of production. Capitalism is incapable of "going green" because it relies on the profit motive.
You do realize that the world economy grew 3 percent last year, but emissions stayed constant? Seems like disproof of your pat assertion right there.
Decarbonization and a market economy are of course compatible, so long as the proper incentives are in place. Those proper incentives being, of course: Pigouvian taxation of externalities; restriction/protection of natural non-renewable resources; and investment in public goods such as mass transportation and basic scientific research. Naive "unfettered" capitalism, of course, inevitably leads to disaster– but not so for a mixed economy, where there is a role for both evidence-based planning *and* price signals.