Amortised inference enables scalable learning of sequential latent-variable models (LVMs) with the evidence lower bound (ELBO). In this setting, variational posteriors are often only partially conditioned. While the true posteriors depend, e.g., on the entire sequence of observations, approximate posteriors are only informed by past observations. This mimics the Bayesian filter---a mixture of smoothing posteriors. Yet, we show that the ELBO objective forces partially-conditioned amortised posteriors to approximate products of smoothing posteriors instead. Consequently, the learned generative model is compromised. We demonstrate these theoretical findings in three scenarios: traffic flow, handwritten digits, and aerial vehicle dynamics. Using fully-conditioned approximate posteriors, performance improves in terms of generative modelling and multi-step prediction.