In today’s world, as a practical matter, wearing non-leather sneakers are much more comfortable than wearing leather shoes. So why is that required on Tisha B’Av? Obviously, I am not all questioning halacha in the past, but, just as mentioned above, a practical matter today.
See Mishna Brura (614:5) in regard to Yom Kippur who on the one hand quotes the opinion that as long as it is not leather says that it is not considered a shoe. On the other hand, he brings the opinion of those who are more stringent and say that one should only use footwear with which he feels the ground. (Such as a thin slipper).The Mishna Brura sees this as the preferred choice. There are those who say, that Tishah B'av is more severe than Yom Kippur for there is an issue of feeling discomfort. (Rav Shlomo Zalman Oirbach zt"l Halichot Shlomo pg. 433) and therefore one should refrain from wearing such shoes. However, many Rabbis are of the opinion that one may be lenient in the case of such footwear. (See Chazon Ovadia Dinei Ta'aniyot pg.299,Ki Ba Moed, 102, Peninei Halacha, Tisha B'av pg.193-194). In summary, comfortable non-leather shoes are permitted on Tisha B'av, however it is praiseworthy for one not to wear such comfortable non-leather shoes on Tishah B'av, rather shoes in which one feels the ground.