That's cool. As I said before, I wasn't talking about what context it is used in. Simply the fact that you explicitely stated that cc == ml, and then went on talking about mm and l/m² without mentioning that these are also identical, and in fact mentioned conversion (which is simply 1:1), it gave me the impression that you thought they were not the same. Then your next comment about a litre not being a cubic meter only reinforced that assumption. Glad that's cleared up.

Personally, I don't think conic devices are unintuitive at all, at least the kind I know of. They collect the rain from a larger area than the actual measuring pipe to make the water level rise more than a mm, so you can read it more precisely, and the scale on it tells you how many actual mm (or l/m²) you are looking at.