The origin of Petaelectronvolt (PeV) astrophysical neutrinos is fundamental to our understanding of the high-energy Universe. Apart from the technical challenges of operating detectors deep below ice, oceans, and lakes, the phenomenological challenges are even greater than those of gravitational waves; the sources are unknown, hard to predict, and we lack clear signatures. Neutrino astronomy therefore represents the greatest challenge faced by the astronomy and physics communities thus far. The possible neutrino sources range from accretion disks and tidal disruption events, to relativistic jets and galaxy clusters with blazar TXS 0506+056 the most compelling association thus far. Since that association, immense effort has been put into proving or disproving that jets are indeed neutrino emitters, but to no avail. By generating simulated neutrino counterpart samples, we explore the potential of detecting a significant correlation of neutrinos with jets from active galactic nuclei. We find that, given the existing challenges, even our best experiments could not have produced a > 3σ result. Larger programs over the next few years will be able to detect a significant correlation only if the brightest radio sources, rather than all jetted active galactic nuclei, are neutrino emitters. We discuss the necessary strategies required to steer future efforts into successful experiments.