A wall would deter people from coming to begin with, which would ease the burden on border patrol facilities, making the whole situation more humane.
Let's not belittle these people by pretending that they don't have access to the internet and world news. People will still come, but once word spreads that a wall in key locations is actually being built, at least some percentage of them will reconsider the decision and settle with aid from countries such as Mexico, which had already been granted to them.