That is, are counters (助数詞) an open class of words?
If yes: Is there an example of a counter that was added recently (say, post-Taishō) and is now in current use by a community of speakers (i.e. not a single writer)?
If no: When did new counters stop popping up in the historical record (that is, when was the last period during which counter-words were an open class)? There were precious few counter-words in Nara-period Old Japanese (-chi, -ri, -ka, "pillar" -hashira for gods), and there's an awful lot now; therefore the class must have been open at some period. The standard hypothesis seems to be that the Heian-era influx of Chinese influence expanded usage of counters (by influence of Chinese classifiers/measure-words); but did they stop adding counters soon after, or did they keep expanding the set up until later periods?
For this question, I'm interested in grammatical counter-words like 個、匹、本、羽 etc. A counter-word doesn't just quantify general measures, as in "3 kilos of flour/lettuce/uranium" or "3MB of data/bandwidth/free memory"; it's also bound to specific sets of words, effectively dividing the lexicon into classes, which it counts in natural units (small animals are counted as 匹, except rabbits which are lumped with birds into 羽, while roundish objects are counted as 個, etc.). Counter-words are also distinct from nouns like ダウンロード in 一万ダウンロード、 in that they can be used to count different nouns in syntactically anaphoric constructions like: