Base 12 and base 10 are related to base 2 in a very similar way and both require the same type of conversion from and to base 2. From the point of view of computers, there is no real difference between base 12 and base 10. Base 12 might be easier for human use, not computer use.
What would fit computers better might be the bases that are powers of 2 like base 8 and base 16, but they hold no real advantage over base 10 for us.
Yes base 2 is related to base 8 as base ten to 100s. But base 8 cant give so much advantages as you outlined about 12 in day-to-day arithmetics.
The other problem I see about changing to any other base is that even if our children learns it, they will need to be in an isolated world to use it. If some body mastered to base 12 writes the figure 10, it means twelve to him in base ten but to me it means ten. This would rather be a confussion between the older and younger generations.
Anyway, your post is superb and I see every point you made to be true.
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Yep, switching now would be a huge pain and would create more problems that it would solve. :) Despite the fact that base 12 is objectively better, the difference and the benefits would simply not be large enough to warrant a transition.
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