Niknak is absolutely right. The SEP restriction is imposed by the planning authority (council). Interestingly, single-engined helicopters are allowed, and practice approaches are currently approved in SEP (but you can't land, which makes me wonder what the legal situation would be if an SEP had an engine failure on a practice approach).
I too hope that SZD is opened up to SEP, even though I'll still fly out of Netherthorpe (keeps me current on short field landings)!
In theory it could open up a new era for Sheffield if single engine ops are allowed. The only real hope for the airport is as a business airport (ideal as it's close to the city). Scheduled services are no more, and NikNak is right that any hope of this resuming will disappear if and when Finningley goes ahead.
In theory Sheffield has a significant catchment area (probably equal to that of EMA) but the short runway and the disappearance of BAE146 (and it's derivatives) from many airlines means that options from Sheffield are limited. Finningley's potential many-thousand metre runway would mean that airlines could operate to wherever they like, from the same catchment area.