Any train from Sheffield would have to reverse in Doncaster, but would not have to cross the ECML 'on the flat' . There are lines S from Doncaster which cross the main lines by a bridge.
As an independent in this discussion, unlikely to use either airport, I would say that the market will decide.
Clearly, no-one would now build an airport where LBA is; but many other UK airports are also in the wrong place - BRS, LHR...
DSA seems, from what I have read, to have created a viable freight business exploiting its long runway.
Several posters have stated that many people prefer using DSA. If so, operators will launch more services.
At some point, the big decision will face the owners: do they invest in much more substantial terminal facilities.
The tipping point would be if a major player moved in.