OK, now sharpen the corners of the fence rail posts so they are engineered to cut anyone that tries that stunt.
I agree, a fence isn't perfect.
The only way I say that a fence isn't needed, though, is if we abandon the ENTIRE welfare infrastructure in our country. Then I'm fine with open borders (aside from terrorism concerns). No social security, unemployment. Eliminate the entire notion of an SSN so that identity fraud is meaningless. And require voters to prove citizenship by presenting a valid US Passport, along with a valid state ID that demonstrates proof of residence in the precinct. No lesser forms of ID allowed whatsoever.
A fence is a good start.
A fence with knife-shaped support beams and weight sensors to tell if someone's climbing it is even better.
A fence with knife-shaped support beams and weight sensors to tell if someone's climbing, then land mines on the US-side is going to stop 99.9% of all illegal immigration after the first kaboom hits the news.