...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.
Let me answer the question by following @HRSE's explanation and recommending a good reading. Eaton and Kortum (Ecta, 2002) use homothetic preferences, a convenient assumption to get a tractable general equilibrium Ricardian model of trade. However, there is exhaustive evidence that the income elasticity of demand varies across goods and that this variation is economically significant.
Fieler (Ecta, 2011) follows Eaton and Kortum (2002) and makes substantial theoretical progress by introducing non-homothetic preferences. High income elasticity goods have a higher dispersion and are produced in high income countries. This higher dispersion leads to more trade among the high-income countries relative to low-income countries. The production side still assumes perfect competition.