my two 125s have no rectifiers. just the coil pickup and cdi with kill switch.
That's because your system has it built internally or designed that way.
The KLX was originally designed as a street bike with lights for other countries.
That being said, they made a harness and electrical system to deal with said lights and accessories.
The lighting coil and pulsar coil need the rectifier to control the amount of voltage to the system.
Kawasaki found it easier to just keep the rectifier as opposed to making a whole new ignition system for the KLX. re production cost.