> I thought (bigger die ^ bigger wires -> more current -> higher consumption).

I am not a semi expert but bigger die doesn't mean bigger wires if you are referring to cross-section, the wires would be thinner meaning less current. Power is consumed pushing and pulling electrons from the transistor gates which are all of the FET type, field effect transistor. The gate is a capacitor that needs to be charged to open the gate to allow current to flow through the transistor. discharging the gate closes it. That current draw then gets multiplied by a few billion gates so you can see where the load comes from.