Well, that's a thorough explanation!
It's only going to be 100% useless if 100% of the illegals are using tunnels. Instead, a wall would mean that 100% of the illegal entrants would be FORCED to use tunnels. Also, the fact of tunnels existing does not mean there is absolutely no reason not to stop the easier methods of breaking the law. Putting bars or a screen in front of a cashier does not stop a robber with a gun, but they do stop thieves from grabbing the money or the register or brandishing a knife or bludgeon. If the overland access is stopped, it is easier to concentrate on finding and stopping the tunnels. They can also deploy methods to find tunnels, which will be a lot easier if they don't have to worry about encountering a violent party of border jumpers while patroling with seismographs or ultrasound machines. A wall would allow firefighters and park service personnel to respond to areas near the borders again. It would prevent border crossers from starting fires to distract the border patrol, and due to violent attacks on fire fighters by such people, they are unable to respond to fires in areas near the border without police protection. The Forest Service instructs firemen not to let the border crossers see them use their radios, because they are prone to attacking anyone they see with a radio out of fear they will call the police. At least a wall will cut down on random encounters like that.

Only an idiot sets up a wall and assumes he's safe. There is a military aphorism that goes something like "an obstacle not covered by fire isn't an obstacle." But while it is possible to climb a high fence with a ladder, if the wall is high enough, getting down intact on the right side is a different proposition.

So what does that have to do with anything. I live closer than that to a major Hispanic population center. That does not mean I am an expert in anything to do with it. I that close to New York City, but that does not make me an authority on what crime prevention and law enforcement tactics will work in the city.
Aaaaand...? This is also a problem. You're making a straw man argument against the position that absolutely no one takes, namely that a wall is ALL that is needed and will solve all illegal and legal immigration issues.

That might be something other than a toothless bromide if Democrats were willing to compromise on ANYTHING. While the occasional individual Democrat might deviate on a particular vote, they are pretty much in ideological lockstep. The big issue difference that came up in the Democratic debates was Bernie Sanders getting crap for the NRA giving him a D-, compared to Clinton's and O'Malley's Fs. What compromises did they make on Obamacare? They left some particularly egregious things out for the vote, and then stuck them back in. What is their compromise on immigration control? Where do they compromise on abortion? Their position is everything pro, with zero respect for other people's freedom of conscience or preferences. Religion is more popular than Planned Parenthood, but they take the no taxes to support religion thing all the way to teachers confiscating and throwing out Bibles children carry in school, and forbidding a sports team to pray in their locker room before the game, or put up religious messages on memorials to dead students. The most extreme Republican on the abortion side in recent years agreed with allowing it in cases of rape (which makes no sense from the position that an abortion is a human life - if a fetus is not a person, there is no reason to oppose abortion, but a person does not stop being a person because they were conceived in rape), but tried to split hairs in the cases of real vs. fake rapes. And considering the rash of fake rape hoaxes in recent years, that could arguably be a legitimate concern. But "mainstream" for the Republicans is a position that makes no logical sense, and for the Democrats, it is "everything is allowed, and sometimes we make you pay for it!"

Yes, the laws are not going to last if the Democrats don't feel compelled to uphold them once they are in power, but a wall would be something they'd have to actively work to tear down, and there would be pictures of that. They could not pretend to be trying to secure the border if they are tearing down the wall. If their rhetoric about the wall being useless is sincere, they shouldn't WANT to tear it down.

Anyway, illegal immigration is a problem because it is a problem. This is not an aesthetic issue of "too many brown people", it is a legitimate threat to the safety of the country and its people, as well as a major drain on the economy and contributing to the disregard of law and legitimate authority. Fussing around about the most nuanced or acceptible response will simply allow that condition to continue. Worrying about satisfying the most people has been done to death for fifty years. Trump and Cruz, who have almost nothing in common that distinguishes them from the rest of the Republican presidential slate, together won 80% if the GOP vote, with Trump getting the most votes for the Republican nomination in history. If that's not a mandate, what is? Why were all the people showing up at his rallies chanting "build the wall"? There is plenty of support for walling off the border, Israel has shown that it works in the modern world, and all we have had is duplicitous talk from candidates on both sides, trying to deceive a general public overwhelmingly in favor of halting immigration, while appeasing wealthy donors with an everflowing supply of cheap labor, that is kept cheap by replenishing the pool and keeping the supply high and demand low.

As for the legal entrants, that has nothing to do with whether a wall will stop the illegal entrants. I certainly have not made a distinction between legal and illegal immigration as a problem, so citing the legal troublemakers only proves my case.