Of course it isn't a legit reason. 99% of all people in the U.S. that doesn't have a permit to stay wouldn't even be stopped by a wall since they flew to the U.S. The wall is just a big misogynistic, racist project to siphon off as much taxpayer money as possible to some of Trumps business associates in the wall construction business.
It would be much, much cheaper to just pay the people without permits money to get a permit and make them stay.
Walls and punishment doesn't drive crime down. Wages aren't driven down by Mexicans, but by rich pig millionaires who refuses to raise the minimum wage but engorges themselves on fantasy wages paid out of the public taxes.
On the contrary, If someone was serious about crime and low wages (and they are not, the people who really are in power just want wages lowered, never raised) they would raise the minimum wage so that people can survive on them wages. That will generate more wealth and more jobs and drive crime down. It's proven time after time in country after country that trickle down doesn't work, the only thing that works is trickle-up.
Unfortunately for the whole world, I think the U.S. is a lost cause.