@Cosmic
The Italians do have their own tobacco, lots of it. They have their own cigar industry for one thing - both Italian Kentucky leaves usually made into cheroots, or something unique grown near Venice they make into Nostrano del Brenta cigars. The trouble is that like coffee, tobacco has been produced by certain key nations, usually linked to Imperial interests.
The Netherlands are the home of the EU's favourite brands of instant coffee, machine made cigars and rolling tobacco - all linked to Dutch imperial and mercantile history. The Spanish have their own cigar industry with their own leaves in the Canary Islands, founded by people that came back from Cuba. The Italians have a very big and quite unique cigar industry too, as we already mentioned, using both home grown and imported tobacco. The Filipinos also have an industry similar to Spain (again founded by those with links to Cuba). Indonesia and Brazil both provide lots of inexpensive tobacco in a similar way to Vietnam supplying the robusta coffee market, as well as prized cigar wrappers. Then there's Cameroon and Malawi in Africa, growing tobacco (often for our pipes e.g. some of the burley in Solani Aged Burley Flake) and harvesting meerschaum (I think in Kenya?) almost like Cote d'Ivoire grows cocoa beans. In addition to the famous Honduras, Dominican Republic and Nicaragua there's unique tobacco, mainly used in cigars that I can think of, coming out of Ecuador, Peru and Mexico. Germany is also a key player in EU tobacco, like the Dutch and the Danish.
The thing is, once you consider there's a strong tobacco industry (blending as well as producing, if not growing) in the Netherlands, Denmark, Germany, the UK and Ireland, it's hard for other countries to compete, especially if these industries were founded off the back of empires and colonialism