Not to sound like a "bleeding heart" liberal, but understand that the $24b per year in money that flows into Mexico from individuals living in the U.S. is money that goes to their families. The document even goes so far as to remind the reader that there is no social safety net in Mexico, which will compound the effect of cutting off income from family members living in the U.S.
It's weird that you prefer the people who have broken your own laws to enter your country, to the ones who have tried to go through your lawful process and failed. Where is your bleeding heart for all the would-be immigrants who tried to go were rejected by your legal immigration officers, who similarly might have no social safety net?
You cannot treat all of the world's ills as your own. You may have decided that illegal immigrants are part of the American identity, but a lot of the voters for Trump have not, and are rallying against that. Unless you convince them to treat illegal immigrants as part of their own, it's unlikely you'll find a "bleeding heart" argument to persuade them.
My heart bleeds for the women and children living off wired money in Mexico, not for the men working illegally in the U.S sending them money. The families back in Mexico with no safety net are the ones who will suffer if we cut off Western Union as a bargaining chip. That is an argument made in that document in favor of the plan. People will suffer in Mexico, so Mexico will be more inclined to make a payment for the wall. The people suffering in Mexico - what law have they broken?
I haven't decided that illegal immigrants are part of the American identity, but I do consider the people not in America who are receiving money to be innocent bystanders (with the exception of drug money, but the cartels wouldn't be stopped by these sanctions anyway).
I see your point, and I see your concern. However, I don't think that concern alone is a stopping factor for implementing such a decision. That would mean that you cannot make progress in many bad situations, when people have begun to rely on them. As an example, I think Obama was right to pull out of Iraq, but he was criticized for increasing the instability there and the return of terrorist groups to it. The Republican support from the Rust belt is a similar example(moving from cheap to intellectual labor has been great for the USA's overall GDP, but has destroyed the livelihood of blue-collar workers).
That was the heart of my point - with a limited budget of resources, you simply cannot help anyone. At that point, you are faced with some philosophical questions - should I be maximizing some global 'goodness' factor, or should I be working for the local group that I am supposed to represent? In the end, the leaders of democratic countries are elected to represent the will of their voters, not to better mankind(unless that is what the voters want!).
If Trump and his supporters believe that a wall will improve the situation for the US and American citizens, then I don't think arguments about the welfare of others(whom they might even view antagonistically) will sway them.
I found different arguments much more persuasive - arguments that removing illegal immigrants would not bring jobs back to American citizens, because they were a net economic positive and creating demand as well as supply.
However, these arguments seemed to be drowned out by the loud, resonating narrative on how evil and racist the supporters of Trump's policy were, which I can only imagine hardened their resolve to get it through. An especially easy angle that Trump could pursue was the disregard of rule of law by illegal immigrant supporters, which I feel could have received a lot more attention and understanding from Trump's opposition.
Is that who we are?