<p>A recent study by Louca and Pennell (2020) spotlighted model congruence (i.e., asymptotic unidentifiability) in phylogenetic diversification models, transforming analytical practices. An unanswered question is whether congruence is ubiquitous, implying that other phylogenetic methods warrant reconsideration. Herein, we investigate State-Dependent Speciation and Extinction (SSE) models, widely used to assess trait effects on diversification. Our findings indicate that unidentifiability is universal in SSEs due to hidden states commonly used to correct for unobserved factors. Notably, every trait-independent scenario is congruent with an infinite set of trait-dependent scenarios, precluding reliable hypothesis testing. We propose an analytical solution that resolves this issue within a congruence class—a set of all unidentifiable models. Additionally, we demonstrate that the discovered congruence is the only possible type, and with our solution in place, model unidentifiability does not compromise macroevolutionary inference with SSEs. What actually challenges hypothesis testing is the model selection across congruence classes that has high false positives. This issue has long been recognized but unexplained. Congruence provides a clear answer: it arises from model misspecification and a previously unrecognized phenomenon of model proliferation. Our results suggest potential ways forward and outline a general methodology for studying congruence in Markov models.</p>