The design calls for the longest single span suspension bridge in the world. By a lot. It also needs to hold up to powerful storms.
The other alternative would be a pontoon bridge. The one in Seattle crossing lake Washington is 2km long, so that would work (https://en.wikipedia.org/wiki/Lacey_V._Murrow_Memorial_Bridg...). However, The Straits of Messina are one of the most active shipping lanes and the maritime traffic is more valuable than the road traffic. The pontoon bridge works in Seattle because the main port is in the Puget Sound and there isn't any major shipping in Lake Washington.