And the Gemara in Masechet Berachot teaches us that when a person puts on their shoes in the morning, they say the Beracha (blessing), She'asah li kol tzorki (Who has provided me with all my needs). Today, we make all of the Berachot at once, not necessarily connected to the actions. But we learn from here that the Beracha, She'asah li kol tzorki, is connected to putting on shoes.
So the question is: Do we say this Beracha on Yom Kippur and Tisha B'Av, when we don't wear our leather shoes? So Hacham Ovadia made two arguments for why we should recite the Beracha. First of all, people wear other types of shoes, maybe not necessarily leather shoes, but they wear shoes made of other materials, and so the Beracha is still applicable. Additionally, he argued that even when one does not have one of these particular events applicable to them, they still make all of the Berachot. For example, the Gemara says that a person makes the Beracha Ozer Yisrael B'Gevurah (Who girds Israel with strength) when he puts on a belt. What if he doesn't wear a belt that morning? He still makes the Beracha because he's making the Beracha on minhago shel olam, on the way of the world. And so, even though on that day we're not wearing leather shoes, we make it in general for what the way of the world is. There are some people who might have foot injuries that put it on, and so in general, we make the Beracha. Therefore, he argued that the Beracha should still be recited on Tisha B'Av and Yom Kippur. However, the Syrian custom is to omit this Beracha. Most of the Syrian sources say that since there's a debate, Safek Berachot Lehakel (Doubtful blessings are treated leniently), and they don't recite this Beracha. Have a great day.