You probably should have let her wear the wrong shoes. Wearing the wrong shoes is uncomfortable. You denied her the minor suffering of wearing wrong shoes.

It's the same thing as why parents should advise kids not to play in the snow in a t-shirt but then let their kids do it anyway if their kids insist; their kids need to learn through literal physical experience that sometimes the results of their choices feel bad.

You make the kid wear a coat and they learn that parents make kids wear coats. You go, "Okay, if you insist on not wearing a coat, go ahead," and they learn that they were wrong to ignore you because they feel horrible and cold. One of the most important aspects of parenting in the younger years is letting them learn that ignoring your advice leads to results that feel bad.

It leads them to trust your judgment later on, since they have an entire library of memories about how it was a mistake to ignore your advice.