Why can't solve tumor clonality using simple EM (Gaussian mixture) instead of MCMC(PyClone) or variational Bayes (SciClone)?

Question

[CY]

SciClone uses variational Bayes; an extension of EM. PyClone uses MCMC; an alternative to variational Bayes. Both method are related to, but more complicated than EM.

Why can't we just use EM (Gaussian mixture) to do this (latent variables is the 'membership' of each variant with specified VAF to specific cluster. parameters are for each Gaussian distribution)? Is because the computation burden or other biological complication / assumption?