This is intended behaviour. If drawing unit is 'None', the real size of the drawing is unknown by the CAD or not defined.

A drawing cannot be converted to or from an unknown unit as the required scale factor for that conversion is also unknown. Somewhat philosophical...

To create a unitless drawing, you can simply set the drawing unit under drawing preferences. This does not change any other aspects of the drawing than making it unitless.

Thanks Andrew for the explanation.

I guess the reason for not being on the same page is based of your knowledge what is going on underneath the hood of QCAD.

Without knowing that my understanding is: If from / to "None" is offered in the CU dialog then I should be able to use it. But it looks like there is no scenario where it works.

Would it work I would expect this outcome:
A drawing in e.g. Inch converted with CU to None should replace below Drawing Preferences the Drawing Unit to None and the Dimension Size scale factor with 1. This does not change any other aspects of the drawing than making it unitless.
A drawing in None converted with CU to e.g. inch should replace below Drawing Preferences the Drawing Unit to Inch and the Dimension Size scale factor with 1. This does not change any other aspects of the drawing than making it to a inch drawing.
A drawing in e.g. Inch converted with CU to e.g. mm should replace below Drawing Preferences the Drawing Unit to mm and the Dimension Size scale factor with 25.4. Like as it already is handled - it will change other aspects of the drawing regarding to the new unit.

In my opinion - this functionality would make the CU tool "round". No need to use a different route over Drawing Preferences ... ;-)

Just my two cents.