Why are three-bladed helicopters relatively rare?
Like with propellers, the blade count on a helicopter rotor is a matter of disk loading. Light helicopters get away with fewer blades. Complexity and losses increase with blade count, so helicopter designers try to fit as few blades as possible. However, this would result in huge rotor diameters for heavy helicopters. There are reasons to keep the diameter small:


Blade root loads due to centrifugal forces
Tip speed: The advancing blade will experience transsonic effects earlier if the helicopter flies in cruise the larger the rotor is. This will limit top flight speed.
Blade bending on the ground. The blade needs to be stiff enough to clear the tail when the rotor spins up.


Now let's compare a few helicopters. I used the technical data on the linked Wikipedia page and divided the maximum take-off mass by the area of the rotor disk:


Sud Aviation Aloutette II: 2-bladed rotor. Disk loading 19.6&nbsp;kg/m². Disk loading per blade: 9.8&nbsp;kg/m².
Bell 205 / UH-1D. 2-bladed rotor. Disk loading 25.6&nbsp;kg/m². Disk loading per blade: 12.8&nbsp;kg/m².
Aérospatiale AS-350 Écureuil: 3-bladed rotor. Disk loading 25.07&nbsp;kg/m². Disk loading per blade: 8.36&nbsp;kg/m².
Bell 412: 4-bladed rotor. Disk loading 34.6&nbsp;kg/m². Disk loading per blade: 8.65&nbsp;kg/m².
Sikorsky S-65 / CH-53: 6-bladed rotor. Disk loading 50.2&nbsp;kg/m². Disk loading per blade: 8.37&nbsp;kg/m².
Mil Mi-26: 8-bladed rotor. Disk loading 69.6&nbsp;kg/m². Disk loading per blade: 8.7&nbsp;kg/m².


I guess you see the trend by now. The UH-1D is the odd man out, but it also stands apart due to its unusually high blade chord. Normally, the ideal loading per blade seems to be between 8 and 9&nbsp;kg/m², and a little more is deemed acceptable if it allows the designer to get away with only 2 blades.

There is no conspiracy to suppress three-bladed rotors. It's the overall compromise between performance and efficiency which determines the number of blades on a helicopter rotor, and the main driver is mass.