Historically the drive towards monoethnic/cultural armies are relatively recent, and though other countries armies by their very size (or lack of the same) could obviously not have the vast number of different ethnicities as the Soviet Union other countries had to different extents as well. To be able to keep some kind of coherency the "ethnic" armies would typicalle be led by upper officers the dominant group (ie. Russians in the case of SU). In the Soviet Union apart from the ethnic dimension there was also a great focus placed on making sure that the troops were made into (and kept) loyal soviet citizens so political officers worked hard on enforcing political discipline in addition to the focus on normal military discipline inherent in any army.

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The army was a mirror of Soviet society in it's mistrust for ethnic groups considered (with reason or simply because of paranoia) to be wavering in support for the socialist endeavour. Belonging to a group that was "less trusted" meant a larger risk for punishment for real or imagined crimes, groups that were "not trusted" say Volga Germans or Chechens would be deported, even actively serving soldiers, just because they belonged to a group that had fallen from favour.

There is an excellent article dealing with this question and works as a starting point if you check the references:

Juliette Cadiot, « “Russian army, non-Russians, non-Slavs, non-Orthodox: the risky construction of a multiethnic army. Russia, USSR” », The Journal of Power Institutions in Post-Soviet Societies