Blazars are promising candidates for astrophysical neutrino sources. Multi-messenger lepto-hadronic models based on proton–photon ($p\gamma$) interactions predict spectra that peak at high energies, whereas statistical searches often assume a power-law shape, emphasising lower energies. We investigate how these spectral assumptions impact neutrino--blazar associations by incorporating physically motivated spectra into our Bayesian point-source framework. Using recent predictions, we analyse 10 years of IceCube data and identify five candidate sources. Our results show that $p\gamma$ spectra suppress low-energy associations but may enhance high-energy ones. Strong associations then imply that energetic neutrino events likely have much higher true energies than those inferred under a power-law assumption. This is particularly relevant in light of the recent KM3NeT detection of the highest-energy neutrino, reinforcing the need for theory-driven models to interpret multi-messenger signals.
For the first time we include angular systematic uncertainties in our fits and show that they have a strong impact on the results and subsequent interpretation.