Making a choice to consume as an individual is different from supporting a policy that would affect everyone. Taxing consumption and fossil fuels does have a lot of support. People are willing to reduce their quality of life if everyone else does as well, but their not willing to make the choice not to consume as an individual if everyone else can continue to do so.
A billionaire has the power to affect policy in a way that the average consumer doesn't, and is more likely to use that influence to make themselves richer than to push policies that benefit everyone.
A billionaire consumes less of their income and invests more than a regular person. Wealth is power, but virtually everyone would spend on the same things.