Earlier quoted context omitted.
Here's the base 12 multiplication tables: https://math.tools/table/multiplication/base/12 It doesn't look more or less nice to me than the base 10 version. Can you describe what is supposed to make it look nicer, especially to aliens?
In base 10, the times tables for 2 and 5 are easy because they divide 10. If I want 2*7, I know 7/5 is 1 remainder 2 so it's 10+2*2=14. As for 5x7, I know 7/2 is 3 remainder 1 so it's 30+1*5=35. In base 12, there are similarly easy rules for 2, 3, 4, and 6. Doesn't seem like that great of a trade off but it could be beneficial. That also just comes down to 12 being a "superior highly composite number". If I personall…
And an even deeper insight is that it doesn't really matter that much and isn't worth shaking up the whole world to change. We're not going to be better or worse at math because of our number base.