Yet this is just what Bohmian mechanics asserts. Remember, we can generalize Arthur C. Clarke's "any sufficiently advanced technology is indistinguishable from magic" to "any physical effect we don't understand is indistinguishable from magic." I believe Bohm showed that quantum mechanics does admit the interpretation that a particle does always have a definite position and momentum, but it requires adding another layer to the theory, it requires a "pilot wave" to shepherd the various possible trajectories into acting as though they were indeterminate about those quantities if one can't see what the pilot wave is doing. Of course, a more standard interpretation of the situation is that if you can get rid of the pilot wave by invoking indeterminacy, and the pilot wave has no measurable consequences, then this is what you should do, and that's what you are doing. But there is no observation that tells us "the particle does not have a definite but unknown position and momentum at any given time."
For the same reason, perhaps we should just say "there is no empirical evidence that it makes any sense to use the term 'path', and little but a kind of classical prejudice motivates its use in quantum mechanics. Of course, some view classical prejudices as a good idea, it really depends on personal preference."
Yes, the notion of purely
classical trajectories is definitely out the window. But pilot-wave guided trajectories are still possible, we just don't know and might not get to know.