Over the next 100-200 years, every (poor) 3rd world country is going to continue to get more and more industrialized and impact the environment more and more. Maybe I'm 100% off here but i'd be surprised if we (rich countries) can lower our emissions enough to offset the increases elsewhere in the world. And limiting the increases of "their" impact will directly effect "their" quality of life improvements unless "we" step in and aid them with more complex (expensive?) solutions. Likely at the expense of any domestic improvements that could be done without added cost of that aid.
Dealing with climate change will include costs and sacrifices that affect individuals and societies. Politicians unwilling to deal with these costs, for ideological and / or electability reasons, will not in my opinion be likely to advocate for the measures necessary to address climate change.
(Also, I'm assuming that when the billionaires go to Mars they won't make the mistake that is common in Stephen Baxter's Scifi novels, where the colonisers always seem to include a subpopulation of disaffected criminals / lowlifes / etc who inevitably mutiny.)
We already know that wealthy people generate the most carbon. If that activity was taxed and then the money was given to poorer people who can't afford to transition to clean energy, it would still be a net win, because it will reduce emissions while making sure it doesn't unfairly affect the poor.
The great thing about statistics is you can maneuver them to support your conclusion. Here's some that support mine: in real numbers, "The United States spends more on national defense than China, India, Russia, United Kingdom, Saudi Arabia, Germany, France, Japan, South Korea, Italy, and Australia — combined."
https://www.pgpf.org/chart-archive/0053_defense-comparison
That's a lot of money to fight pirates.
Public perception may be one reason. If a carbon emissions tax directly leads to big increases in fuel costs, it can cause problems for drivers / vehicle users for whom fuel cost is a significant concern. The 2018 Gilet Jaune protests [0] in France were partly due to public dissatisfaction with fuel price rises. Regulatory instruments (such as fuel efficiency standards) are more opaque and may obfuscate the connection between between political decisions and the inevitable price rises.
[0] https://en.wikipedia.org/wiki/Yellow_vests_protests