While the cams may be there to also help stamp out police corruption, there is another large problem that they attempt to solve.
Insurance fraud is more common than I had even thought in Russia; and some insurance companies require drivers to have a dash-cam. There are hundreds of videos/compilations you can watch online of people literally jumping in front of cars to try to get insurance money out of them. The dash-cams record these events by the hundreds (not only in Russia) and are a large reason the dash-cams are so prominent.
They are fairly comical to watch as well.