For fun maybe, but the maintenance workload would be more trouble than its worth.
After the new Wall is finished, we have been rotating military units through to run a few coils of concertina on the back side (American side) of the anti-climb plates at the top. It makes it way harder to climb over with ladders or ropes, and lasts for many, many years untouched.
The image of these walls with the remnants of invaders hanging in the wire with the vultures cleaning up is enough to give an old man a woody...
Where is that wall located?