I always assumed a Markov chain was some kind of Siberian drinking game. Hence the interest in the running the chain to its stationary distribution.
Calculating the stationary distribution is one of the main things people do with Markov chains. That's all that PageRank is -- the stationary distribution of the Markov chain constructed from the network of links on the web.
Markovs is a natural law, proven, is it not? Well then, it will be found in any system.