Why there won't be electric rocket (yet)?

The only way that a rocket can move (that we have discovered yet) is to expel mass in one direction to travel in the other direction. This is done by burning fuel that gets shot out of the back of the rocket. There is no way (unless EM drive works which i’m sure it does not in this context) to move with purely electricity, some exhaust matter is always needed. That being said, there are ion engines that use noble gasses and electricity to gain very high efficiency propulsion. They are too weak for launches and can only be used in space.