Hansard - both the Twin Otter operation and the S61 helicopter are not cheap on the seat cost front. The Twotters just about stretch to Bristol/Southampton with limitations. Bigger aircraft (facilitated by more runway length) means lower costs, better connectivity further up the country towards London and beyond. I think the French would quite like a connection too.
Of course if the islanders want to keep out the 'riffraff' by maintaining the limitations imposed by having to use small aircraft and limit the volume of tourists, that's fine. I suspect however that there are islanders that wish it wasn't so expensive to escape and island-based businesses that would wish to see a few more visitors on the islands.
Islanders need to debate those pros and cons, then, if it's to be a longer runway, work out where the money comes from and the return on the investment. Again, who would pay if the latter?