Why gaussian assumption in GMM-HMM ASR?
One reason Gaussian distributions are assumed is that it simplifies modeling since a Gaussian distribution only has 2 parameters to estimate (i.e., mu and sigma) and the properties of the distribution are well understood.
Gaussian distributions are often a reasonable assumption for acoustic data since acoustic data can modeled as a sum of independent random variables. According to the central limit theorem, the normalized sum of independent random variables  tends toward a Gaussian distribution.