As long as we have laws that grant them a hearing once they set foot on our soil, detection of their illegal entry is meaningless.
A simple and effective change in the law would be to make it apply to legal entry only…at an authorized port of entry. There are many (near 50) of these along the southern border.
A better place to apply for asylum would be at the American embassy in their home country. The embassy could have a staff to investigate the claims made for asylum.
In the US claims cannot easily be investigated as thy can say anything.
Nobody … not even Trump … claims otherwise. But if walls didn’t work (in the same manner as the lock on your door,) nobody would build them except as landscape features.
Besides, when coupled with electronic surveillance, the Border Patrol knows exactly when and where you leaned your ladder against the wall and will be waiting for you when you climb to the top.