Why don't helicopters prefer shorter rotors with more blades?
The rotor works by accelerating air downwards, therefore creating an upward reaction force on the blades that lifts the craft.

The lift force is equal to

$$L = \dot{m}\Delta v$$

where $\dot{m}$ is mass flow rate through the rotor and $\Delta v$ is the change of speed of the air. To accelerate the air to that speed, it has to give it kinetic energy. This requires power

$$D = \frac12\dot{m}\Delta v^2$$

(the induced drag).

Now a rotor with smaller diameter will be able to affect less air, so the $\dot{m}$ will be lower. To produce the same lift, it will need larger $\Delta v$ and therefore it will need more powerful engine (up to a point, because longer blades will have higher form drag that will eventually outweigh the reduction in induced drag) and, more importantly, burn more fuel.

The blades, like wings, affect air to a significant distance above and below them, so you don't need many blades to use all air within the rotor area. But no matter how many blades you add, they will still only affect the air within the rotor area, so the efficiency won't change much.

As far as tiltrotors go, they have relatively small rotors and that makes them awfully inefficient in hover. But they don't spend most of their time hovering, they spend most time flying somewhere and in the fixed-wing mode they are faster and more efficient, which outweighs the worse efficiency during take-off and landing.

See also: Is there any equation to bind velocity, thrust and power? (via Energizer777's deleted answer).