Those are the goals that drive it, but it is not what is "all about". It is also "about" making and selling goods and services to consumers that they want, and it is "about" providing jobs (and wages) for people, and providing pensions for them when they are old. Amazing, when you think of it, what profit and dividends can achieve.
I'm not sure why you mention absence of regulation. Just about everyone knows capitalism needs regulation. Most people, at least those of us who have experience of working in a business, are aware that it is heavily regulated (competition law, employment law, environmental regulations, health and safety at work, the myriad rules about financial conduct, intellectual property law, advertising standards, data protection, and so on.) All this is as it should be. I don't think I have seen anyone here question the need for any of this.
Government now needs to add some more rules, to guide businesses far more strongly towards minimising greenhouse gas emissions. (Apart from the obvious help for sustainable technologies and so forth, a carbon tax is one way of applying incentives to all business activities.)
Regulation is crucial because it enables a business to say to consumers, "Sorry, we can't sell you that product any more" without the consumer simply going off to buy it from a less climate-aware supplier. That makes it a level playing field for all businesses, which overcomes the problem of competition and customer choice driving the continuation of bad habits.
Businesses will moan about a carbon tax, due to the extra accounting they will have to do to calculate the carbon (and methane?) footprint of their activities, the cost of which will mean higher prices for us all, but if government is firm they will knuckle down and do it.