These fares do require decent flexibility -- for tourist destinations, you won't be leaving on a Friday and returning on Sunday. The £4.49 flight between London and Romania is on a Wednesday, on a Friday it's £60-70.
Ryanair use the low fares for marketing, pretty successfully. They probably expect many people to add luggage (£10-40, depending on route), or buy food on the plane (£10+) or be disorganized and end up paying more.
In Western/Northern Europe they use out-of-the-way airports -- London Stansted is 47 minutes by the fastest train from London, or over an hour by car. They have a reputation for reducing the fees they pay the airport by threatening to move to alternative airports, unless they're given a very good deal. People walk to the plane, they don't use jet bridges. The whole plane is economy class, and the seats plasticy-fake-leather, which must speed up cleaning. At airports, they'll usually use the worst (farthest) gates. All the planes are the same, so maintenance is simplified and pilots easily moved around.
As to why the US doesn't have them -- I don't know. Norwegian is a budget airline, and has fares like New York to Paris for $175 one way (Tuesday, no luggage, no food!).