LEDs give off heat too, but since they only emit light at one frequency, there is no wasted energy, all the energy goes into monochromatic light, none into heat. Sooner or later, though, that LED light hits something, gets absorbed, and it is reemitted in the far infrared: heat. An incandescent filament only puts a small amount of its energy as visible light, most is given off as IR, what we perceive as heat. The LED is highly efficient in terms of illumination produced per unit energy consumed, but you still don't get something for nothing.

Getting kinetic energy directly out of energy, without intermediate working fluids, would be wonderful, though. But there would still need to be something to carry away the excess momentum. The momentum in the whole system is conserved, so the momentum of the moving vehicle has to be counterbalanced exactly by the equal and opposite momentum of the exhaust gases. Without them, the drive you propose would violate a fundamental principle of mechanics.

Consider a projectile falling in a gravity well towards a planetary surface.
As it picks up speed it's momentum increases. But the planet is also attracted to the projectile, and falls towards it. mV = -Mv. Again, the total momentum of the projectile-planet system is zero.

Maybe there's a way, but right now, conservation of momentum looks as solid as conservation of energy. It's not just a good idea, it's the law.