Shortly after Stalin's death, on March 5, 1953, Soviet film crews were instructed to picture the national mourning all over the USSR. This resulted in kilometres of film, shot in the highest quality available at the time.
A few years later Stalin fell off public grace, and these films were stored & forgotten.
About 60 years later, Sergey Loznitsa worked his way through this extensive material, and produced this excellent documentary about Stalin's funeral and the national mourning around it.
Loznitsa's choices are historically correct, and the fine shooting of the 1953-Soviet film crews does the rest. You should also remember that the Russian way is somewhat slower than our way - they take their time to do things. And so does Loznitsa.