Nothing says "arbitrary" more than a quantity that was deliberately rounded up 9km just for the heck of it. Things can be guided by math/logic and still have arbitrary elements. The Karmen line definition is a logical definition with certain arbitrary constant selections, and therefore it's not specific. This doesn't mean it's random, only that there are band of valid definitions.
It's correct to state a boundary defined by centrifugal force dominance is somewhere between 80ish and 100ish km, and the specific number is somewhat arbitrary. It's not correct to say its for 20km (for example), which would be a truly random selection.
The specific identifiable altitude still requires an arbitrary selection of lift coefficient and vehicle mass in order to calculate. The calculation is vehicle dependent, not general. The values used in the original definition of the general case were set to be "typical", which yielded 91km. Because of the arbitrariness of this definition, it was defined to be 100km as that was "more memorable"
See above