Every flat tax is fraught with issues. Now a huge number of people who can barely afford transportation simply can't anymore. So much has been spent subsidizing roads and by proxy suburbs over 70 years, and any plan will have to involve helping people trapped by those ciecumstances, or they will overturn those plans democratically.
In short, some people can afford to pay for climate change fixes, and some can't. Any solution will simply have to be progressive and have a fair, equal burden on everyone.
This is the beauty of carbon taxes - in addition to creating incentives to avoid carbon emissions, they raise revenue. That raised revenue can then be directly given back to people. Wether you do so according to 1/(number of people) or some means-adjusted distribution is an exercise i will leave to the voter.
If the goal is to reduce emissions, then a tax on emissions is the only solution. Anything else is too open to avoidance (just look at corporate tax avoidance).
Maybe there's other ways to make it better for the people who can't afford it - a tax free allowance they can claim back or similar.
I'm still not sure if this is feasible across borders though. How can you stop carbon tax havens?
There are only two ways to reduce transportation emissions: do less transportation or introduce less emitting ways of transportation. If the poor are exempt then everybody is exempt because more money can only mean more freedom of choice, not less.
In short, some people can afford to pay for climate change fixes, and some can't. Any solution will simply have to be progressive and have a fair, equal burden on everyone.