Yes, I agree that the allegedly-sexagesimal notation of the Babylonians is better thought of as a sort of compound alternating-base system. That seems inelegant enough to me that it's not at all obvious that 60 is a better choice than, say, 12.

Note, by the way, that the same things get terminating expansions in base 30 as do in base 60, it's just that some of them take longer to terminate. (Just as fractions like 1/16 terminate in base 10, just more slowly than they do in base 4, 8, or 16.)