The answer is pretty simple. The damage caused by externalities is not born by the producer so there is no incentive to stop causing damage. Once you create the incentive everything will work itself out without government intervention. That's the beauty of the free market.
However, the reality is that people like the current situation and prefer government intervention in favor of carbon emitters. This unfortunately leads to situations where subsidies to e.g. coal based electricity generation have to be matched by subsidies to zero carbon electricity generation just to have any impact at all.
Alternative technologies already exist but there is no reason to use them because conventional technologies are blessed by the government. Of course you can forcibly pump money into them and eventually get the result you desire but only at a higher cost.
In Germany people absolutely disliked the idea of a revenue neutral carbon tax where every tax payer would receive a share of the collected tax back at the end of the year. Instead the government introduced a minimum price on CO2 certificates which is basically the same thing except it is not revenue neutral but hey at least it's not a "tax" so the uneducated mob won't come after you. People think they understand taxes but when you show them something "complicated" like a cap and trade system they suddenly don't understand a single thing.