All this is necessary to achieve this is wider application of so called "mild hybrid" technology. Think over-sized battery, over-sized starter motor, over-sized alternator, drive by wire throttle, and a bit of ECU smarts. Any time the car is stopped (or below speed X, where X is small 3mph? ) the engine is "off" (no fuel, no spark, engine still turning if the car is in motion), and the battery and starter motor move the car. Once the speed threshold is exceeded (or battery is sufficiently low) fuel and spark are resumed. At any greater speed the vehicle is powered entirely by the engine.
Having electrically powered accessories (power steering assist, air conditioning, brake booster, etc.) would be preferable, so that all of those systems still function when the engine is not spinning. It addition, making these electric tends to increase efficiency and reduce weight. If these systems remain belt or vacuum driven there can be many situation where the ECU may be forced to leave the car idling, or waste battery power spinning the engine to keep the accessories running.