"Because there's no airport and it takes a round trip of at least 2-3 hours from Doncaster to Sheffield,["]
... from the web link.
It doesn't.
Sheffield airport flights to 'business' destinations didn't make a profit, and DSA will not attract that sort of traffic either. So it's off to MAN or the Eurostar - whose relocation to St Pancras incidentally makes the train option for Europe more attractive from both Sheffield and Doncaster, especially if Eurostar and/or DB realise their plans to have services extend beyond Brussels in the next few years.