Don't claim to know the real story behind the coin. My guess is that Russia, like some other countries at that time, experimented with making a cheaper more durable minor to keep up with growing demand for coins. Silver was still in relatively short supply in Russia at that time. A few years earlier Russia exchanged a large quantity of gold coins for silver minors minted in Paris.
As to displaying bust of Alexander I on the coin it is likely due to his role in Napoleon's defeat and restoration of European order. In 1870, European order was once again shaken, and the coin displaying Alexander I could have been a gentle message from Alexander II...