My point is whether there is such a context, in which "you will show" would really change the meaning if it is substituted for "you will have shown".
In the sentences:
After we've seen your performance, you will have shown us your talent.
After we've seen your performance, you will show us your talent.
the first sentence implies that the "showing of talent" takes place as part of the performance. The second implies that it will happen after the performance. So the meanings are different.
"You will have shown" is a phrase using the future perfect, which is normally used when describing an event in the future to show its relevance with another event in the future, or when describing an action that will take place before some specified or predictable time. The time could also be specified by a previous sentence, or clause.
By then, you will have shown what you meant to do since the beginning.