JonasBackthat is a very very common complaint about CEC. Although it is an industry standard, the way it is interpreted by each manufacturer is different. It is frustrating for the video industry as a whole as CEC was supposed to help make a standard of the control protocol. At Crestron, we actually give our programmers the ability within our tools to just send the commands over the CEC bus for the simple reason that you might need to change from standard CEC to actually control that display. You can see here what all the different manufacturers actually call their version of CEC.
I wish "Off" truly meant off and "On" meant on, but this is no different than even control in the days of RS-232. "Off" on some of the displays in the early days meant turning off the RS-232 port which meant there was no way to turn it back on. So its a battle that has been around for a very long time.
Just inserting CEC of on and off is going to be hit or miss for any combination of display and device. If you find one that works, my suggestion is to stay with that model and even on that firmware if you can. Firmware in displays will also change behavior sometimes so you need to be careful.