Ok, but do you see what I mean about how that part was just sitting there without any explanation? That's why I find it hard.

Is the question really why we train children on basic arithmetics in base 10?

That could be meant shallow or deep. The shallow answer is because that's all you need to do to function in society (and conversely, while arguing with a police officer about the presumed base on speed limit signs may be fun, it is also pointless).

The other answer probably needs to explore the question a bit further. Perhaps a good starting point is the fact that we almost universally share the physical characteristics of having ten fingers.

Wildberger has a channel that explains this from scratch, also shows a different method of long division https://m.youtube.com/playlist?list=PL5A714C94D40392AB

His method for polynomials/derivatives is also interesting if you watch until the end, dead simple calculus.