So Soviet characters that speak English with a slavic accent would be less distracting? Surely if you are bothered by this they should be speaking Russian with English subtitles.
I think we have seen this sort of approach succeed in a major US TV production in Netflix's Narcos. There are English-speaking characters, yes, but most of the drama happens entirely in Spanish.
I think this series would also have been better fully in Russian with English subtitles.