It's actually the reducing of the alumina (aluminum oxide) to metallic aluminum that takes huge amounts of electricity. And as mentioned, that is done with carbon electrodes which are consumed in the process, leading to relatively high CO2 emissions. Though yes, if that electricity would be produced by burning fossil fuels the emissions would be even higher. So it's not like there aren't big benefits to doing aluminum refining in Iceland, or other places with low-emission electricity.

There is some R&D work going on though to do this reduction step without CO2 emissions using other electrode materials, see e.g ELYSIS.