You have no empirical data that wall heads just “appear” more efficient.
I already made three statement, centrifugal fan, lack of condensate pump and line set length(friction losses) that do affect efficiency.
I apologize, I did not realize you had listed centrifugal fan, lack of condensate pump and line set length, as advantages. You are correct, these are all absolutely efficiency advantages during testing, and sometimes in real world applications.
Centrifugal VS Propeller
Correct, centrifugal/wheel fans are arguably more energy efficient, particularly with high, constant air flow, but with lower, variable airflow (inverters) that efficiency can easily be lost. During testing, with a constant load, a nice, clean new wheel fan may be more efficient. But what about a five-year-old, wet, mud/mold caked wheel-fan compared to a dry, dusty prop-fan? Probably not. In any event, it's the condenser using the bulk of the power, what kind of fan does it have?
Condensate Pump VS Gravity
Correct, a condensate pump is less energy efficient than a gravity drain. One unit mounted on an exterior wall, with a gravity drain running out and down will use less energy than cassette unit that depends on a pump to evacuate the condensate. But as soon as you have to add a condensate pump to an interior wall unit or want multiple wall units to utilize a common drain, that savings is gone. Gravity drains are also more likely to clog, but that's generally much less of an issue in the US.
Line Set Length
Correct, longer lines use more energy than do shorter lines. A wall unit mounted on an exterior with the condenser on the opposite side of the wall will generally have shorter lines than a cassette unit. But a wall unit mounted on an interior wall typically will not, nor will a wall unit in the front of the house with a condenser on the back of the house. And what about multi-splits?
There is no point having a logical discussion about your “theory” when all available data points to the opposite of your “theory”.
I think you mean all available sales literature, yes?
HVAC equipment is a well developed science and the engineers that develop the equipment are well equipped to measure its efficiency. They are not just pulling numbers out of a hat.
This is absolutely correct. Manufactures are in the business of selling product, and good test results are means to that end.
In a 20' X 20' room, a new wall unit on an exterior wall with the condenser on opposite side of the wall one will use less energy than a cassette unit in the same room. But it will not cool the room more effectively, as it generally blows from one end of the wall to the other, as opposed to blowing from the center of the room out to the perimeter of the room.
What often ends up happening, is people run a wall unit and a ceiling-fan to better distribute the air, so all the extra efficiency of the wall unit over the cassette are lost.
You don’t even have any numbers to pull out of a hat, you are just giving general ideas.
Yeah, sorry, I'm just not that good at regurgitating sales literature. You're welcome post up a lot of numbers if you like, or you could explain how it is I am wrong in my thinking.