Why did the popes begin issuing encyclicals? It appears as if heavy duty instructions to the world at large began with Pope Leo XIII in the late 19th century.  

How did it come about that he issued so many encyclicals?  Did he set a precedent for future popes to emulate in their teaching office? 



Check 'em out for yourself
That is actually a fairly accurate assessment. Most of the documents which came out of the Vatican were Papal Bulls, and they would be one, possibly two, per papacy. You can find most of them at papalencyclicals.net. Unfortunately, we didn't even bother keeping the documents from Gregory the Great through until the Renaissance (poss. later, you can find the exact information in the book Europe: A History (sorry, I am far too lazy to go through the relevant 200 or so pages to be more specific)) Leo XIII changed that. (Don't know if it was the assertion of infallibility, the Immaculate Conception, or what), but since then there have been exponentially more documents released by the Vatican.

Of course, it could have to do with the fact that not only was in inexpensive to print documents (the offset press was invented 8 years before his election), it was also possible to transmit data across the Atlantic in real time (the trans-Atlantic telegraph cable was first laid in 1866). Though it might also have had to do with the declarations of Vatican I. Though the teaching authority of the Roman Pontiff had been long established, this was (as near as I can tell) the first time that the authority was so clearly laid out.

And then another reason he might have written was the Holy Spirit (he's always makin' mischief).