The reason existing law is not enforced, is because it's broken and unenforceable.
Now, we can continue on or change. While no system is 100% secure, and electronic system is far more secure then a paper and pencil system.
my only thought would be......
the reason existing law is broken is because existing law is not being enforced....but this is my opinion.
The reason the law is unenforceable is that our borders are unsecure, and law enforcement agents are being actively discouraged from enforcing it.
Build a complete physical barrier, and enforce the law. Then, and only then, will the problem get better.