There's an analogous affront to our naiveté when we go from (nonrelativistic) classical to quantum mechanics, though, and it's one we can completely resolve: the question "where is the electron?" in, say, the double-slit experiment doesn't have a well-defined answer, but the electron does have a state, and using that state you can read off the probability of finding the electron in some region of space at some specified time.
Similarly, although we may not be able to answer the question "how many particles are here right now?", is there some way to represent the state so that it contains some information about something I might conceivably care about, as we could do in QM? It seems strange to me that the end of the story would be "It's complicated, don't worry about it," especially if we're going to be making statements about what the state "looks like" if the interaction is "weak enough"; without knowing what's doing the looking-like I have trouble even understanding what such a statement means.