Level running lines primarily are used with shooting heads attached to them for distance casting. Salt water fly fishing is where I see this set up mostly.

I also see these level lines used quite a bit in Great Lakes tributary steelhead fishing where significant weight is used on the leader to get the flies down to those bottom hugging winter steelies. The skinny running line has less resistance to the water flow and gives a better drift. The significant weight provides the momentum to make the cast and shoot the running line.