TUI seemed to operate successfully from Doncaster so I wonder why others failed.
TUI are an interesting point. Thomsonfly as was in 2004/5 (when it was announced they’d be the launch carrier) had dipped their toes into the low-cost seat only market. They offered a number of city destinations at launch from DSA including Dublin, Amsterdam, Prague and ISTR Paris. Pretty solid decision by Peel, an established operator with a wide scope of holidays and business friendly city destinations, with the added bonus that it would mean Humberside offering would be significantly reduced, weakening its position. They also closed their base at Leeds which meant that if you were in Yorkshire/Lincolnshire and you wanted a TUI holiday you’d be going from Doncaster. Worked for them, but holiday flights and daily high frequency city pair schedules are much harder to maintain as they require a pretty substantial catchment area to sustain them.
EasyJet ran a season of daily flights to Geneva in the first winter of Doncaster operations. That never returned owing to lacklustre support. When they closed their East Midlands base, it made perfect sense to have an operation at Doncaster, as there was then no easyJet flights from any airport on the M1 corridor between Luton and Newcastle! This time they tested the market by out-stationing one aircraft at Doncaster and flew to destinations such as Prague, Amsterdam, Barcelona, Palma and Faro. Sadly 5 months into the operation easyJet announced they’d be pulling out, a study of the passenger statistics highlighted that their best month at Doncaster saw and average load factor of just below 70%, Faro and Palma thought to do reasonably well but the others struggled to fill half an aircraft on average. Similar occurred with FlyBe, poorly supported but they were subsidised by Peel. Ryanair never really made a serious attempt at Doncaster because of their bases at East Midlands and Leeds (which opened after Doncaster opened!). Jet2 and KLM couldn’t be tempted.
So I know a long answer, but in conclusion for Doncaster to work, the airlines would need to pull out of Leeds Bradford or East Midlands (or both). But they have much bigger core markets than Doncaster so m, with the exception of TUI, the airlines didn’t do this.
I hope this helps answering your question.