While there indeed might have been enhanced vehicle stability at high speeds due to tail fins, from a practical standpoint, they were mostly a styling gimmick. I should add that one justification I saw in a car hobbyist magazine when tail fins were new, was that stylists could alter their shapes from one model year to the next to freshen a design. That indeed happened.
I discussed early tail fins here, including Chrysler Corporation's 1956 models that were a transition from 1955 not-fins to the 1957 redesign that included fins as a prominant, basic feature.
As for the fin fad, it rapidly faded during the early 1960s.
Just for fun, the present post poses the question: Which American cars had the tallest tail fins when the fashion was at its height?
Chryslers and DeSotos had the simple fin design shown here for model year 1957. The corporation's Plymouths and Dodges featured more elaborate designs. The high point of the fin appears to be a short, but noticeable, distance above the cowling at the base of the windshield. (Note that the lower edge of the body is essentially parallel to the lower frame of the image, the car being nose-heavy.)
An example of another brand's tail fins. These seem to be a little lower than Chrysler's, though still prominent.
There is a Cadillac, the brand that introduced decorative tail fins on its new 1948 design. The fins seen here are clearly taller than Chrysler's.
Now for some rear-quarter views. This looks like the Saratoga in the photo above. The fins appear higher from this perspective than from the side view.
Side view of Cadillac fins on a convertible. In recent years, they have become a cult-object, epitomizing the excesses of 1950s American styling. That aside, they strike me as being ridiculous, a last-gasp of Harley Earl's declining abilities as GM's styling vice president before he reached mandatory retirement age.
