Why is this
transcribed like this
It seems much more obvious to me to fit it into 3/2 time:
Maybe the clue is in the 'split common-time' symbol? But perhaps it didn't have the same meaning in those days?
This is an example of mensural notation, common in the 14th and 15th centuries. You are correct that the clue is the split common-time symbol, which was one of the symbols (along with the common time symbol) that carried over into modern notation. (By the way, this wasn't a "c" for "common," rather it was an open circle for "imperfect" time, meaning a breve divided into two semibreves instead of three.)
Imperfect time is generally translated into 4/4 time, whether there's a line through the C or not. While this particular tune may work as a 3/2 melody, that isn't the intent given by the notation. If it were intended as 3/2, the time signature would be a circle, optionally with a line through it.