Yes. SEM assumes that all relationships are linear and that all variables are normally distributed (for standard errors and fit indices calculations). Those ass

Yes. SEM assumes that all relationships are linear and that all variables are normally distributed (for standard errors and fit indices calculations). Those assumptions are baked into the model and are usually never discussed. Non-linear models are not common in social sciences so that's probably why I never used them. There are a few variables that are usually quadratic (like the effect of age on wages). Other than that, linear relationships are good enough most of the time. The only real application of non-linear model that I have seen are generalized structural equation models (GSEM). These allow for the use of link functions in SEM (logits, logs, poisson, exponentials, etc.) and are the multiple equations analogue of generalized linear models. I am not familiar with structural causal models (SCMs), but a quick google search shows that these are a non-parametric version of SEM based on Baysian estimation and are a generalization of Baysian network. They sound cool but I don't think that they will become mainstream in psychology research anytime soon.