If we had free energy, would people be required to work anymore?

Free energy means unlimited labor systems. It means all deserts could be made to bloom through unlimited fresh water distillation and pumping. It means food and factory production could be free as arid areas would be green and fertile. It means transportation could be free. It means excavation of raw materials could be free, as deeper and deeper holes could be dug. It means housing could be free via robotics. It means the only use for oil would be for lubrication, and even that would be synthesized. It would mean a clean, green planet. It means space exploration and colonization. If free energy is possible, as the sun has free energy and it a chemical process, isn't the search for free energy the direction we should go?