[thaumasiotes]

> Even in Chinese, which supposedly has no count nouns, there a few places when you do just count things directly.

Are those things nouns? Days, for example, must be counted directly, except that the grammar is very clear that 天 is not a noun at all.

月 can be used with or without a measure word, but the obvious analysis would be that it is a noun if used with a measure word and not if counted directly, much like 人.

(Preemptive counterargument: is "right" a noun or an adjective?)