What you say doesn't quite correspond to quantum physics as it's known. Quantum physics is quantitative and precise, so it's difficult to say there's something undefined there. It doesn't suggest nonlocality, absence of hidden variables means only absence of hidden variables. It doesn't suggest antirealism, if only due to precision, you can say it doesn't work how you want, but at worst this makes it unintuitive. Conversely Dirac formalism works as if quantum state exists in itself in precise form, which has a good compatibility with basic macroscale intuitions about what "physical reality" means.
But quantum physics can't predict exactly where the individual dots on the detector will be, only their distribution. That does not sound totally quantitative and precise and defined. You would not accept such predictions for macroscopic objects :)
At least it shouldn't be nonlocal just because of the erroneous rumor that Bell proved that quantum physics is nonlocal or because randomness, nonlocality and retrocausality are just directly observed.
Would you be satisfied if the theory clearly states: "At the time of measurement, the position of the photon interaction is determined by randomly sampling from the quantum distribution"?
