Distributing the revenue is not about compensating for harms. It's about ensuring that you don't have a net impact on people who are using the typical amount of energy. The idea is that the tax captures the externalized costs of economic actions, like emitting carbon. Once the cost of the actions is fully priced in, it is reasoned, consumption will decrease to the optimal level given the harm done by consumption.

The biggest problem with this idea is that we don't really know what the costs are going to be.

In practice, poor people would be beneficiaries of a externality-capturing tax, because by and large, rich people use a lot more carbon. More flights, bigger cars, bigger houses, etc.