There are always the local codes to deal with concerning local permits and border “right of away easements” and Etc. You could do this but making the connection to the existing fence easement would be impossible without fed approval. So they would just pass through this gap between the two.
And even these local governments can be controlled by the feds through funding extortion. Look at what happened to my state of Az a few years ago when we tried to enforce immigration laws on our own as a state. Obama’s fed sued us and threatened to stop all fed funding to our state. And it worked... We had no choice but to comply or die as a state.
Nice to know you have a problem for every solution.