Despite what they say, they don't really compete with legacy carriers, they just target their passengers. There's a difference.
They
really, really do compete with legacy carriers, they took an enormous amount of passengers from exisiting legacy carriers who felt they were being ripped off by BA. At LGW, people stay with BA for Avios and complain about the complete lack of onboard service. Unless a lounge is an absolute for you, a huge amount of the exisiting market uses EZY over BA when spending it's own money, which allows EZY to run a frequent schedule to be attractive to business. What you mean is they don't do connections, however given P2P is a huge part of legacy business and EZY are taking it from them, that's clearly competing.
Your analysis mixed apples with pears.
As businesses, the legacies are stagnant,
Or in terms of KLM and say BA, the short haul operation supports the more profitable long haul, they're co dependent and in good years, the profits roll in. Aviaiton is notoriously loss making btw. When you say stagnant, that does rather ignore the aggresive cost cutting measures BA have taken to put their cabin crew costs into line as near as possible with the market rate. A network carrier will always have big overheads, but they're slightly different business models.
In terms of market placement, Ryanair are still going to be positioning themselves as cheaper than EZY, but moving away from the growth spurt as an ULCC. The business models are moving closer and the overlap will increase but there's still going to be a distincitive place in the market for both. I think this discussion is a little focussed on STN which in terms of EZY alone is the loser out of a LGW/LTN/STN/SEN sandwich.