One thing I would stress is that there is not one "true" system of units that is correct in some absolute sense. Unit systems are to arithmetic as type systems are to code. It's OK to have different systems of units that are good at preventing different kinds of error. This means that when talking about

That being said, you can absolutely criticize any given unit system, just as you can criticize any given type system. And some of your criticisms* of SI are indeed valid. (*Out of those that I even understand at all.) It just means that when we compare unit systems, we should be focusing on factors like: what kinds of errors do they catch/prevent? How understandable are they? How reliable? You do that in some places, such as your excellent point about torque vs. energy. But it's less clear why we should be splitting out the 3 kinds of units or only ever specifying number of apples as integers (I can certainly have half an apple) -- how does this actually help us? I would also argue that if you're trying to say something like "1 Apple + 1 Orange != 2", then I'd argue for the same reason that "1 Apple + 1 Apple != 2", because different apples are different sizes, shapes, value, etc. Really I'm just not clear on almost any of your points about "discrete units".

And for the geometric units, why stop at 3? We obviously could have 4-dimensional angles as well (possibly not physically useful, but maybe for spacetime calculations ... and why should our system of units only apply to our particular universe?). You could have n^2 and n^3 units similar to logarithmic units (e.g. 1 squart = 1 foot, 2 squart = 4 feet, 3 squart = 9 feet). I'm not claiming any of those are useful, but I am claiming it shows that your examples are not "fundamental".

> The electromagnetic wave corresponding to its output signal provides the unit of length in its wavelength, the unit of time in its wave period.

But aren't the wavelength and period of an electromagnetic wave linearly correlated by the speed of light? Doesn't this make your 3 fundamental dynamic units only 2?