Why is electricity not transmitted wirelessly?

Power is transmitted wirelessly in many applications, just not where transmission efficiency is high importance. And that is the reason it is not done more: efficiency. At low frequencies, galvanic (that means metal) conduction of electricity is many, many, many orders of magnitude more efficient than, say, air.

At higher frequencies, one can use electricity to create E-M waves which travel well in air (or even space); but the problem is that the medium in which they travel is typically 3D (rather than the functionaly 1D path in an electric circuit), so the stuff spreads out a lot and the receiving station only gets a very small fraction of it (your car or home radio, receiving a signal from a braodcast station, is an example).

Techniques have been and are continually being developed to force power to travel in a 1-D manner, instead of 3D, in air without wave guides. Some successes include phased array RADARs, lasers, microwave antennas for telecommunications, Yagi antennas, and parabolic dish antennas. However, no commercially viable technique has surfaced to move large amounts of electrical power over long distances without long stretches of metal.

Electricity is the flow of electrical charge - generally electrically charged particles called electrons in a wire. It can't flow through air, except in the form of electrically charged particles of air - as in a spark or lightning stroke.

Magnetic fields can travel in air, so you can send electricity by using it to make a magnetic field and then using the magnetic field at the other end to make electricity. This is how a transformer works - but it only works efficiently if the two sets of wire making the magnetic field are very close.

You can use it for sending small amounts of electricity a short distance where a wire (or connector) would be difficult, such as charging an electric toothbrush - but it's not efficent for large amounts or a long distance.

It can be done via electromagnic waves. The higher the tansmission frequency the better. Tesla wanted to do it. But is is very inefficient, much of the power will be dissapated where it won't do you any good (such as heating the ground), or be poached by non-paying people who have learned how to harvest it. There is some work on antennas that can be used to obtain energy from the environment (mainly radio waves), but these are for very low power remote devices, they are not suitable for bulk power applications.