Now, some decades down the track, the thing I still find most annoying
about claims for the "rationality" of the SI is the bloody kilogram!
If the kilogram is a basic unit, then the gram should be a
millikilogram.

Yep!

That's another example of the basic failing of the metric system: the
"rational" units just ain't the right size!

In a "rational" system, the unit of mass would be the mass of one cubic
meter of water. So the "rational" unit of mass should be 1,000 kilograms
or 1,000,000 grams!

SO: the metric system is "irrational" by a factor of ONE MILLION!