In reply to jon:
You are indeed quite correct, and it was presumptuous, perhaps even a little arrogant of me, to assume that the OP was looking for information on getting to the French side of the hill. For that, I hold up my hands, and truly your forgiveness I implore.
However... given that the three most popular routes to the summit are on the French side, with around 50-70% of people taking the Gouter route alone and, being stingy here, let's say that only 10% try either the Three Monts or Grands Mulets routes (which I can't help but feel is lowballing it a little...), can we assume that around 80% of the 20,000 successful summiters each year have come from France?
Given these numbers, only some of which I've plucked out of my ass just now, I think that without any qualifiers from the OP such as "I am interested in climbing Mont Blanc via one of the less-popular Italian routes, which is the best airport for that?", I don't think it was too far a step to jump to the Chamo-centric conclusion.
(Also, if you want to suggest Megeve altiport as a viable alternative to Geneva, I might just put forward the idea of the helipad at Argentiere... it's closer, people do fly into it... ten minute transfer time to Chamonix... therefore it must be the best option!)