Trying to make LGW as a rival airport for LHR was tried, and failed abysmally, in the 1960s, 1970s and early 1980s. At a time when central government owned both airports, the "second force" civil aviation policy forced to be based at LGW. it should not be revisited now.
The UK private longhaul LGW-based carrier was expected to compete (on a playing-field about as level as that at Yeovil Football Club) with publicly owned LHR-based BEA and BOAC, later BA. There was a succession of them: BUA, BCal, Laker and Virgin.
Not surprisingly, BUA, BCal, and Laker all failed. Virgin survived only because it was able to move its base to LHR on the collapse of the ill-fated "second force" policy.
Both BA and VS retain a presence at LGW for historical reasons: BA because it inherited it on the takeover of BCal, and VS because it started there. It is no co-incidence that both use LGW for mainly leisure point-to-point destinations and keep LHR as the hub for connectivity.
Airport ownership has nothing to do with it. Before GIP bought LGW, airlines were shifting to LHR from LGW when opportunities presented, and that continues today. Expect Vietnam Airlines to move to LHR-4 at some stage and Korean to join the rest of it's operation at LHR.
As stated above, STN has declining pax numbers despite being FR's main UK base, so it would be pointless to have another runway there at this time, or in the near future.
LGW is more than just an U2 base although it's an important part of its business. LGW also does holiday flights and charters, and is a "waiting room" for carriers wanting access to LHR. In that respect, LGW is a hybrid airport, a little of everything.
We go round and round in circles but it all comes back to the same point: LHR expansion is the only game in town.