Why are European low-cost carriers not running long haul flights to destinations like the USA, Asia, or the Middle East?
Some are, Norwegian Air runs a flight from Stewart airport in New York to Dublin Ireland and back. 

One the benefits that LCC's get is from buying only one airframe for their fleet, which can, depending on where they are based limit their range as many fly A320's or 737's. 

The benefit is not within Europe per say but with short, fast turn around, flights that benefit from the general implementation of the hub and spoke system. There are also LCC's domestically here in the USA like Spirit and plenty in Asia as well.