I like interactivity for computer games, but I don't find them useful in research. By their nature they imply individual choice and consequently violate the universality of scientific results. Interactivity is useful in teaching situations (even often overstated) and in interpretative tasks.
On the other hand, I would like a parameter explorer: a script that invokes a given program over and over again with slightly varying parameters. An interactive visualization complement lets me explore the solution dependent on the possibly high-dimensional parameter space.