In 2007 the Civil Aviation Authority recorded that 3.7 million passenger journeys had taken place at Manchester, Liverpool, East Midlands and London airports by people who started or ended their journey in West & North Yorkshire. On average that’s 10,000 trips every day, 365 days a year travelling on the local road network to get to the M62 and M1 to get to other airports.
Not everyone, of course, will have taken a car or taxi. And you're also assuming that the 3.7 million are travelling singly, rather than in groups.
It's also not clear how that 3.7 mill splits between the airports you named. I'll bet the lions share is London and Manchester though.
I realise that this isn't what you want to hear, but not everyone living in Yorkshire can be catered for by LBA. That's not just to do with runway length, weather, topography or ground access, but is also related to demand for various onward destinations. The fact is that London, and to a lesser extent Manchester, will always be able to offer a wider range of destinations than LBA, so some of the local population are going to have to travel beyond the LBA catchment area to find flights to destinations for which there is not sufficient demand in Yorkshire alone.
As Roverman says, it's a market driven business.