Crime is a problem indeed, but I still feel like adding more lighting in hopes of solving this is not really the solution, and like you say, just moving the problem around.
I think lighting very busy areas (think railway stations, main streets in cities) is a good idea in general, but how many areas are really busy at night? And most people aren't outside in the middle of the night or early morning, so most lights could probably be shutdown after the evening is over?