There will always be aircraft specific considerations which should be covered in the type training. This applies even in light aircraft. For example the Lake Amphibians have a high pylon mounted engine and a sudden application of high power can cause a strong pitch down instead of the pitch up pilots would expect with nose mounted engine.
You make an interesting point.
The conversation seems to have significantly departed from the original intent. UPRT when taught in accordance with the EASA guidance materials, does not IMO conflict with what was traditionally taught in the “unusual attitudes recovery” exercise.
There can be little doubt that the basic principles of the stall may be demonstrated well using a light aircraft. It is not the case that UPRT training can be achieved in a light aircraft in my view. Stall recovery is mentioned only as an aside in the various UPRT manuals. The FAA documents and others so far quoted concern themselves very much with the interoperability of the complex automated systems and the pilot. That for me is where the work should be concentrated, and is, because the avoiding and the recovery from the stall by the pilot is not possible when the automation is preventing it or, indeed, is the cause. The error has often been the pilot pushing the wrong button. The training managers of airlines that I have spoken to did not see the value of throwing their pilots about in a Extra 300 as being useful.