Because the power of electromagnetic radiation (energy per unit area perpendicular to the source) drops off proportional to the inverse square of the distance. So, at one unit away it's a reference for full power, at two units it's at one-quarter power, and three units it's at one-ninth power, and so on. This is the fatal flaw with Tesla's scheme: By simple geometry, you're pouring power into space and you need massive input to get any output at all at an appreciable distance.

http://en.wikipedia.org/wiki/Inverse-square_law

The WiTricity project you may hear of does things based on a completely different technical footing, which is more efficient but less broadly useful. For example, with the WiTricity technology, power receivers can't be any more than a quarter-wavelength from the transmitter, which means that they can't be any further away than a few meters. Definitely not what Tesla had in mind.

> You've read enough of Tesla's diaries to know that?

I know enough physics to know that. Tesla's diaries are irrelevant.