The Russians starting position is a long way from the Straits, and while they historically advanced south, they took quite some time doing so - consider that the Black Sea coast was acquired only in 1783 at the annexion of the Crimean Khanate, and part of Bessarabia in 1812. Going from there to Constantinople could be done by three paths: left-side by the Balkans, but the terrain is not that great (marshes, mountains) and Austria is on the way; right-side by the Caucasus, but the terrain is simply awful; and down the middle by the Black Sea, but the Bosphorus is ridiculously easy to fortify, and naval invasions are not really the Russian way of war.

The Russians only seriously threatened Constantinople twice, in 1854 and 1877. In both cases, the Turks defended really well in the Balkans (although the Russians did finally come really close to Konstantingrad in 1878!), and there was also foreign intervention to protect the interests in Turkey. (In particular after the Suez canal, it was totally vital for the English to keep the communications with India, and thus to defend the Suez canal from anyone in general and the Russians in particular!).