PP training in any aircraft should include all aircraft flight control systems, power management, navigation, communication, airports, winds aloft, cross country, and on and on. As already stated, some aircraft are more demanding of trim than others, but you can expose the student to trim in any aircraft. BTW, there are aircraft much more demanding when it come to trim than a Mooney. But it wouldn't make sense to do PP training in a Mooney, much less an Mu-2 or other complex aircraft.
With all that is included in a complete PP training program, we are exposed to a lot of information, systems, and concepts. The fact is few PP students master much of anything, in spite of what they might think. The goal is to produce a safe and competent pilot that can continue learning and master these things as they gain more experience.
Some students can be a bit inaccurate when conveying what they have, or should have learned. I once flew with a PP student near the end of the program on a cross country flight. I asked when were they going to adjust the mixture. The student asked what I was talking about, so I pointed at the mixture and said that control. The student said the instructor told them to never touch that knob.
Fact was, I knew that instructor, and I knew better. This student was scared of killing the engine in flight.
When I hear something that doesn't quite sound right about what an instructor said, I first get out a grain of salt, just in case...