Are vector spaces really the right category? In particular the product and coproduct of vector spaces are isomorphic (both isomorphic to the direct sum).
It depends on what you mean by right category. It is true that vector spaces identify certain constructs that linear logic distinguishes, but it doesn't identify everything so it still has some interesting content. Finding models that don't make unnecessary identifications is one of main lines of research in the field.
They're not the right category for computation, but they are a valid interpretation of linear typing. They're one of Girard's original inspirations for linear logic. The resource interpretation came later.
