Glad you asked this, Rob. The answer is—absolutely not! Storm windows were invented many, many years ago for a very different type of window—a very high-maintenance window. Not sure how young or old you are, but maybe you recall those old windows with all the little panes.
The panes were held together with a wooden frame and putty. The putty would dry out and crack every season, so it was a lot of work to maintain windows. Once larger sheets of glass could be manufactured they resolved the maintenance issue with the concept of “storm windows” that would protect primary windows from all that weather damage. So people didn’t have to reputty and repaint those little frames year in year out. It became popular quickly to add storm windows to your home.
Today we just don’t need storm windows. We have composite or “engineered wood” frames that are both highly insulating and maintenance-free. In fact, I would recommend that you NOT install storm windows over your new energy-efficient windows. What’s going to happen if you do is there’ll be a tremendous heat buildup inside, between the storm and the primary window. You can actually do more harm than good, because everything is just going to cook inside, including the seals, frames, spacers etc. Take your storms to the antique dealer—like I recommend in my article!