Why do so many models assume homothetic preferences? ...when Engels Law, backed by a good amount empirical evidence, demonstrates that overall consumer preferences are not homothetic.

See for example, Jorgenson (1997)
Here a short answer: Homothetic, identical preferences have the modelling advantage that the distribution of income across individuals does not matter for aggregate demand. That is, if you want to study, let's say, monetary policy where you do not expect changes in the distribution of income to affect your policy recommendations, then this is a reasonable assumption to make. If you want to study questions where changes in the distribution of income have large impact on policy recommendation (e.g., optimal taxation) this may be a bad assumption.