Ion thrusters are capable of providing the same amount of delta-V for far less fuel (e.g. Falcon 9 v1.1 second stage specific impulse is 340 seconds, while some ion-thrusters have a specific impulse of over 10000 seconds).
Ion thrusters have excellent life expectancy. NASA's NEXT ion drive continuously operated for over 5.5 years and after that the engine showed little signs of degradation. Rocket motors are not that reliable.
Ion thrusters have been tested and performed very well in numerous space missions, including Dawn, Hayabusa 1 and 2, Smart 1, GOCE, Deep Space 1 and more are upcoming. This concept isn't particularly new or experimental.
Generally, ion thrusters are awesome.
So why don't we use them to lift everything from LEO? They can use ~30 times less fuel, and fuel in space is very expensive. Why do we still need rockets going above LEO for unmanned spaceflight? Why develop super-complicated harsh-reentry capable reusable rocket technology when we can have spacecraft lasting for decade(s)in a stable space environment? They proved to be powerful enough to withstand air drag at very low orbit (only 255 km above the surface of Earth). What are the problems?