Does this benefit them somehow, by only travelling within Europe?
well here are a few reasons off the top of my head.
LCC aircraft carry maximum payload so the galleys are not too big. Flying long-haul requires bigger galleys and possibly more toilets. This wastes space which on aircraft configured for short-haul is used to carry pax. In a nutshell a LCC aircraft can carry more pax.
The average sector lengths are shorter so more turns in a day. Before LCCs you would typically see a 737 or A320 turnaround take around 45 minutes. LCCs can do it around 25 minutes. That is a savings of 20 minutes. If you fly six sectors a day that is additional 120 minutes or 2 hours more that the aircraft can spend flying to make money. On long haul, you can't cut the turnovers much as cleaning and loading catering and cargo takes times.
On long haul you carry more fuel (in fact you carry more fuel to carry the fuel you need) so costs are higher.
The smaller aircraft allows improved frequency .. ie better to fly a small aircraft 6 times a day than to fly a widebody twice a day. This increased frequencies make it attractive to customers.
There are a lot more but these are the major ones..
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.