Yes, bases 12 or 6 bring only a negligible improvement over base 10, which is entirely due to the fraction 1/3 being more frequently encountered in practice than the fraction 1/5.
When the exact representation of frequently used rational numbers is irrelevant, base 2 has no competition.
If you want to represent exactly more rational numbers than with bases 2 or 10, than either base 30 shall be used (= 2 * 3 * 5) or bases that are multiples of 30, like the traditional 60 or like 240, which fits well in a byte.
(Of course any squabbling is instantly forgotten the moment they have to act against their common arch enemy, the Hexadecimal Society)