Why are there extra restrictions on constant-speed propellers?
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.