There are a number of points Plato sought to make with his Cave allegory. The first of which is that it can often times be exceedingly difficult to accept the idea that your entire experience on a particular matter may be completely wrong, and the path of retraining oneself is unlikely to be an easy one. The second lesson of the story is that, as much as you may wish to enlighten others to your newfound way of thinking, they may become defensive about the notion of changing their dogma, possibly to the point of hostility to protect it. The final point is now the would-be teacher has a decision to make, continuing to attempt to persuade others to see things your way, or to accept that they may need to make the discovery in their own time if at all.
Plato went for a theory-first approach, using mathematics to construct theories which he then used to then fit his observations of the world into. Aristotle did the reverse, and used observations to build up a theory of explaining how something worked. It would seem their contemporaries believed the reasonings put forth by Aristotle were both more common sense and better equipped to handle further scientific inquiry, which is likely why it saw prevalence. If I had to choose between being a Platonist or a Aristotelian, I believe it would be the way of Aristotle for me, for the same reasons as his contemporaries took; it makes more sense to use a grounded-theory approach as he seemed to have done.