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The multi-messenger era is now well underway, with high-energy neutrinos providing a unique opportunity to study particle acceleration. Several marginally significant associations between high-energy neutrinos and potential astrophysical sources have been recently reported, but a conclusive identification of these sources remains challenging. We present various strategies to put these associations into the context of the relevant astrophysical source populations. Firstly, we can use the non-observation of point sources in IceCube searches to place constraints on the high-level properties of the unknown source population. Secondly, simulations of proposed populations and their transient behaviour can be used to evaluate the probability of chance coincident detections in a principled manner. Finally, these simulations can also be harnessed to predict the contribution to the overall neutrino flux that is consistent with an assumed source–neutrino association. In particular, we investigate the implications of the IC170922A–TXS 0506+056 observation. We find a chance coincidence probability for flaring blazars and neutrino alerts of 7.5%, ranging between 3.7% and 12% when considering extreme cases of our model assumptions. We also show that we should expect to see as many as ∼32 spatial coincidences between blazars and neutrinos, which is consistent with current observations. Assuming that there is a blazar–neutrino connection based on the gamma-ray flux, we find that the connecting flux factor is restricted to < 1e-3 or < 0.1 when considering all blazar emission or only flaring emission, respectively. Together, these results raise further constraints for the picture of flaring blazars as neutrino sources.