There are a lot of layers to this, and we should discuss some assumptions. For example, an obvious one is that there are exactly about 8 word classes in English and that words "belong" to them. If you do make that assumption and you have criteria for deciding, it's very easy to do this, if you have the time for all 600,000 words. But why would you want to do that? Can you, by categorizing all of the words, accomplish something? That's why we'd need to look a little deeper.
and it can make sense although the lines are sometimes blurred.
That's part of the problem. You can't have something blurry if you want to count it.
A "very rough estimate" seems possible. In fact, we can arrive at that intuitively:
nouns are a very large class, adverbs, verbs, and prepositions are large classes, adjectives is a big class, and pronouns, exclamations, determiners and conjunctions are minuscule classes.
Yes, certainly. That's fairly well known. I don't think you'd find many people who disagree with you about it.
At least etymologically speaking, it should be possible to trace a word back to it's original meaning, and thereby rank the word classes correctly after size – or can it? What's your opinion?
This is confusing. Why are you mixing word class and etymology? There's no relationship there, although you could attempt to statistically analyze how often (and which) word classes change from one to another.
Word classes are properties of lexical items in a specific grammar at one time, not throughout history or space (where they might or might not change from generation to generation or person to person).
Would you care to make a guesstimate as to how many of the 600.000 words pertain to each word class in the dictionary?
It depends on how precise you want to be. Ranking the classes is relatively easy. One quick way of doing this is to use a corpus. Google Ngrams is convenient:
https://books.google.com/ngrams/graph?content=_NOUN_%2C_VERB_%2C_ADJ_Very clearly, there are more nouns than verbs, and more of both than adjectives. Add in the other parts of speech if you want.
Obviously that's actually about
usage including multiple repetitions of the same word, but broadly that's similar to, at least in ranking, the distributions in the lexicon. You could easily (but probably not easily through a web interface) look for only unique items in the corpus and count up how many there are.
If you want to count up everything in the OED, go ahead. It'll look a lot like your list of 15 words. You could, if you wish, take a sample of maybe 1000 words and see what the distribution is like. That'll be a rough approximation.
There may be a way to do this automatically-- the OED does have word classes listed, so you could just count those up on the computer if you can access the raw data properly. They might already have that info somewhere.
But then we circle back to the questions above:
1. Are the labels applied correctly in the dictionary (and could you do any better if not)?
2. What's the point in labeling these anyway?
I believe that anyone who would question whether a rough approximation is possible would do so because
they believe that all of this (the definitions, the existence of classes, etc.) is uncertain.
A real problem with this
in English is the process of "zero-derivation": Google is a noun that became a verb. So is it in one class or two? It's easy enough to
count, but a lot harder to decide why, what and how to count.