One of the lessons learned from the German effort under the heading of Energiewende is the insight that simply shifting to renewables and recommending improving energy efficiency is not sufficient to lower greenhouse gas emissions. Combined with the expected radical change of technologies this requires a more profound understanding of our energy systems. Therefore, in contrast to most conventional approaches we propose a deepened structural analysis that covers the full energy value chain from the required functionalities for mechanical, thermal and specific electric energy services via application and transformation technologies up to primary energy. This deepened structural approach opens and substantially enhances our understanding of policy designs that are compatible with the Paris Agreement and Sustainable Development Goals. We discover the essential role of four energy grids, namely for electricity, heat, gas, and information as the key for integrating all components of a newly structured energy system. Consequently, we conclude that policy strategies focusing on individual components of an energy system as simply shifting to renewables may from a comprehensive perspective on sustainability in the worst case even turn out as counterproductive.