The wikipedia on the SIA points out that it is not an assumption, but a theorem or corollary. You have simply shown this fact again. Bostrom probably first named it an assumption, but it is neither an axiom or an assumption. You can derive it from these assumptions:
I am a random sample
I may never have been born
The pdf for the number of humans is idependent of the pdf for my birth order number
Turns out that some parents do require a mandatory license for parenting. A parent can end up before judge and be required to take a parenting course. These courses are all (as far as I can tell) evidence-based, developed and evaluated using sound science. Programs like: Incredible Years, Triple P, Kazdin Method.
Ironically, most parents, even those who read lots of parenting books, never encounter a parenting book that is primarily evidence-based. Most parenting books are opinion-based. The most recent evidence-based book that I know of is “Everyday Parenting” by Kazdin.