Climate change is a negative externality. The onerous cost of pursuing compensation through the Courts, and the long term nature of the carbon release indicates that it is infeasible to regulate this behaviour through the tort system alone. There is a market for appearing to be green but that still isn't enough, so the only real sensible way to internalise the problem is to introduce a carbon tax at the point of extraction, but distribute 100% of this (minus admin costs) back to the taxpayers.
Sounds sensible, but you are ignoring is the unseen costs of a carbon tax.
How do you quantify the costs and ascertain who has suffered damages? Even the best scientists cannot agree on the extent to which carbon emissions cause climate change, let alone the value and distribution of the costs associated with the damage.
It also implies a need for world government, or at least unprecedented levels of international co-operation since mosts of the costs of climate change will be born outside the jurisdiction where the emissions take place. In particular, countries like Bangladesh and island countries with low lying areas stand to be most adversely affected.
This raises the issue of further problems that are already rife when it comes to foreign aid. Sure, Australia could pay the government of Bangladesh compensation, but how much of the money will actually go to those impoverished Bangladeshis that have been harmed by climate change? More likely the money will mostly be misappropriated by corrupt governments and warlords and actually used to harm the people intended to be helped.
Furthermore, if the biggest polluters like the USA and China don't commit to such a scheme (along with most of the world) then anything done at the domestic level will be almost pointless.
Then there's the transaction costs. Since the government is inefficient, incompetent and corrupt at everything else it does, there is no reason to expect that this would be any different. Already the Australian government is planning to exempt or compensate some of the biggest polluters from the a carbon tax scheme. Then there's the usual problem of the most powerful companies and individuals being very good at circumventing taxes. It's quite difficult to accurately measure carbon emissions, and expensive and time consuming to ensure they are not being under reported.
So like most proposals for government intervention, it sounds good on the surface and would make sense if it could be done at a reasonable cost with reasonable accuracy; but in practice the costs of the scheme would almost certainly outweigh the benefits.