Yeah, I'm not sure why you got down-voted. In the 1890s people that everything was a wave but then phenomena like wave function collapse and the quantum Zeno paradox were hypothesized and observed. To combat this you can introduce mathematical tricks like delta functions but this more of a hack.
Perhaps, the biggest philosophical problem with waves are their integration requirements and the potential for such iterations to exceed cosmic speed limits. When the function is continuous a perturbation at one end must effect the other end.
He's downvoted because he doesn't seem to get what the entire discussion is about, which is on a higher level. Instead he is caught down in the "lesser models". Whenever you have a paradox, like wave-particle duality - but also the "French paradox" in nutrition, it's not because there really is a "paradox" in the universe, it's because the way you look at it is too limited, and if you find a better view you will see there is no paradox. That doesn't make the paradox-creating models untrue - in their context, but we have gone beyond them. That's the subject of the submitted link!
I think the down-vote happens, because he's argumenting too concrete for the question.
I don't know much about physics, but my take on this is:
First you model reality with waves and particles, then you see that particles can behave like waves and vice versa. The next step is to model reality with something different that can behave like a wave AND a particle and suddendly there is no paradoxon anymore.
Perhaps, the biggest philosophical problem with waves are their integration requirements and the potential for such iterations to exceed cosmic speed limits. When the function is continuous a perturbation at one end must effect the other end.