Honest question. Is Sicily actually economically important enough for such an expensive mega bridge? To my mind it would make more sense to invest that money in Milan.
Backwards regions are subsidised by the cities. Sicily can be made into a tourist resort for pensioners.
Or perhaps building a bridge will enable them to bring water in easily from the mainland?
Speaking with the experience of someone who has spent a good half of his life on that island: Sicily's problems are mainly due to the following factors, in this order: culture and mismanagement. Everything else (yes, including the organized crime) comes in a very, very distant third place.
To figure out which angle is more correct, you need to consider facts about the specific regions.
Per-capita GDP is very low for Sicily relative to other regions - but it still has an overall GDP of around $100B, which is similar to Costa Rica or Croatia. Giving it a car/rail connection to the mainland would be a huge boon for the region and Italy in general.