I think it's important to see the railway as a link to London and little else. None the population centres over 100,000 in Essex are linked directly to the airport, other than Rayleigh (around 100,000) and Southend itself. (I am not including London Boroughs within the historical Essex boundary). The railway does little for those in Southend, Basildon, Castle Point, Thurrock, Chelmsford, Harlow, Colchester and Clacton.
At this moment in the airport's evolution, it seems that few see it as a destination, rather it is a departure point for pleasure and leisure seekers. So throwing big money into rail - bearing in mind an express service calling Stratford and Liverpool St only, would probably only shave 6 - 8 mins off the journey - seems pointless.
I am not saying the rail-link is unimportant, without it, it ceases to be a London airport, but short of building a Maglev rail with trains capable of 300mph, I don't see any large scale investment making enough difference to be justified.