Expectation Propagation (EP) is a promising framework in message-passing algorithms based on factor-graphs. The inherent ability to combine prior (partial) knowledge of system variables with channel observations suggests that an effective estimation of random channel parameters can be achieved even with a very limited number of pilot symbols, thus increasing the payload efficiency. Yet, the way in which the probability distributions of latent variables (both data and parameters) are combined and projected often requires ad-hoc adjustments to reach satisfactory performance. Here, we apply EP to a classical problem of LDPC-coded transmission on a strong Wiener phase noise channel and discuss how and why, even in the simple case of binary modulation, EP can fail or succeed.