I think the basic idea is that highly composite numbers [1] make good bases. It's a trade off between the number of divisors of the base and the number of digits we want to learn.
Also it looks like the Babylonian is a composite system, where the 'digits' are represented in base 10 (the 10s use a different digit, but it doesn't matter). They could alternatively use base 12 for this digit.
Note that both 12 and 60 are such numbers.
[1] https://en.wikipedia.org/wiki/Highly_composite_number
Also it looks like the Babylonian is a composite system, where the 'digits' are represented in base 10 (the 10s use a different digit, but it doesn't matter). They could alternatively use base 12 for this digit.