Not that some wealth redistribution wouldn't be nice, but doesn't it have potential to actually increase global carbon emissions?

Actually, it is the other way round and there is nothing wrong about that. In fact it is an essential part of any anti-climate change action. Poor people cannot afford a lot of the necessary proposed taxes on consumption and re-alignment of the economy that is needed to fight climate change so a core component of any action needs to be how to safeguard their living standard while acting against climate change.