Anyone can build a fence. The idea that it will solve the illegal problem "IS THE PROBLEM".
Hell, my dog tunneled into my neighbors yard....about 100 times.
What is ridiculous is your straw man argument.
No, a fence alone will not solve the problem, but a physical barrier is one necessary element of a multifaceted strategy to attack the problem which includes a physical barrier, boots on the ground, air assets, employer enforcement, denial of benefits for illegals, deportation, and a monitoring system to catch visa overstays among other things.
No one thing is going to “solve” the problem. We need to attack it from all directions.
You don’t have to fence the whole border. The wall needs to be backed by mobile forces and holding areas. If 300 people come through in a rush you have to be able to detect them, round them up, contain them, and then return them.
The idea is to make it hard. You don’t have to have the same level of barrier out in the desert where there is no water, towns, or roads as you do in areas where tunnels can leave a building in Mexico and arrive in a building in the U.S.
Humans have been building effective walls for a long time. The Great Wall of China and Hadrians Wall come to mind and there are some pretty effective walls out there now in Israel, Korea, India/Bangladesh.
It can be done. It’s pretty much an open border now. People leave the states for a vacation at home and seemingly return without being inconvenienced at all. That could be changed.