Why are there extra restrictions on constant-speed propellers? Constant-speed propellers are far more efficient than non-constant-speed propellers, allow the engine to be made considerably simpler (due to removing the need to continuously adjust the ignition timing based on how fast the shaft is rotating at any given moment), and, unlike traditional variable-pitch propellers, don't require the pilot to manually adjust the propeller pitch.

However, according to Wikipedia, propellers with constant-speed mechanisms have considerably tighter restrictions on them than other propellers:


  A pilot requires some additional training and, in most jurisdictions, a formal signoff before being allowed to fly aircraft fitted with a CSU [constant speed unit; the part of the propeller mechanism that makes it a constant-speed propeller]. CSUs are not allowed to be fitted to aircraft certified under light-sport aircraft regulations in the United States.


Given that a constant-speed propeller performs its pitch adjustments automatically, without the need for pilot intervention, and that constant-speed propellers perform better, not worse, than other propellers, why all these extra requirements and restrictions?
The engine is the same, not simpler. There is one additional level of complication to the system -- the constant speed propeller has a number of extra parts.

The pilot needs to handle one more lever, selecting the speed. And needs more training in order to remember to put it at the right setting in various flight conditions -- not to mention how to handle an emergency when the constant speed unit falls (you need to prepare for every possible situation).

All in all, more training and more complicated systems sets up the requirements for restrictions.