Not incidentally, 1524mm is exactly 5 feet. Which was the rail gauge widely used in the southern US states. The Russian tsar hired someone who had been building railroads in the US south to design his railroad, and here we are.
The 1520mm was some Soviet effort to "metrify" their railways while keeping compatibility with existing rolling stock.
If I recall correctly, the rolling stock remained the same, tracks were re-railed and the 4mm came from tolerances that were historically very loose. So the stated goal was to get higher speed and stability from tighter tolerances.
I also remember reading a long time ago that there were two engineering schools: one modeled that tighter tolerances would decrease oscillations and vibrations and the other predicted exactly the opposite. I think in the end they settled on natural experiments. Hope I didn't make this up, need to search for sources.
The 1520mm was some Soviet effort to "metrify" their railways while keeping compatibility with existing rolling stock.