Without researching it, I can offer a couple of suppositions:
1. Tuna, in it's various forms, is a very common fish, and many cultures---as far back as the Phonecians---depended on it. To this day, fishing the tuna runs off the coast of Sicily and Sardinia is a major annual event. Salt cod played a bigger role in world affairs, it's true. But salting the fish was no longer required, when canning came about. And the cod fisheries were more tightly controlled than the tuna fisheries.
2. Given its cross-cultural appeal, and the size of the catch, it would therefore have been a logical choice when canning food took off in earnest back in the 19th centuries. And that sort of thing feeds on itself. Canned tuna was purchased because people were familiar with the fish. And, because they were buying it, more of it was canned, which made it more commonly available, so more people bought it, etc.
As others have mentioned, however, other fishes are canned; and not just as a specialty item.
Canned salmon is almost as ubiquitous as tuna, as are sardines. Other common ones include herring and mackeral, and a wide range of shellfish, such as oysters and clams. Canned crab is seen on the shelves more and more as well.
They have taken the oath of the brother in blood, in leavened bread and salt. Rudyard Kipling