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.