There is no medical evidence whatsoever that baby shoes contribute to stronger ankles, period. Baby shoes do, however, keep the feet clean and protected if the tot is strolling around on a public sidewalk--and they keep the feet warm if indoor floors are chilly. But a baby learning to walk is likely to get the hands and the behind all over the floor as well as the feet, so if the little one doesn't need protective mittens, he or she probably doesn't need socks and shoes either. Baby shoes are sentimental and appealing, of course, so you can't blame parents for running out to purchase little shoes for their offspring, whether or not they are necessary. I certainly did this, myself.
There were strong ankles and strong bodies long before there were shoes, and some of the strongest ankles on earth probably belong to the celebrated long-distance runners of Kenya, many of whom prefer to run without shoes.