Chemical lasers(What will likely be used, as solid lasers are basically capped at a few hundred kW right now) don't actually require energy to power the laser itself as it relies on chemical reaction to power the beam but require a very complex system of support equipment(pumps to cycle reactants which are usually gaseous or in liquid form) and cooling equipment to carry away the heat from the reaction. Which is why Polyus weighed 80 tons and was only a prototype of a prototype which was no where near full functionality.
That sounds like swapping out one can of worms (power) for a whole other can of worms (plumbing and cooling).