BKS - a couple of things;
1.) would you really expect a petition to present a fully-costed business case?
2.) let's add a few others to that list of yours - Antwerp, Belfast City, Lugano, Southampton. The number of 'city' airports in Europe is quite small because most big European cities are fortunate enough to have a full-size airport close-by. Sheffield is unusual in being so far from an airport with a full-size runway (let's not dwell on that business about Robin Hood being 20min away... South Yorkshire Police would no doubt appreciate a few more details on that). So Sheffield was at a huge disadvantage until Sheffield City Airport was built.