You are mixing up your 'they's. There are multiple theys each with their own motivations. Frequently their interests align. Not always.
I don't expect anybody with money and power to play by THE rules, but everybody plays by SOME rules. Understand the rules each player is playing by, and you understand the game a lot better.
I don't for a second think Trump's motivation behind deporting people is pure as the driven snow. I'm sure for many people behind that policy, perhaps including Trump himself, there is a lot of thinly veiled racism or not so thinly veiled racism and a bunch of xenophobia too.
That doesn't mean it's impossible that it will work, and bring about some sort of positive result.
For me, the big problem with illegal immigration is it creates an easily exploitable underclass. A group of people who will work themselves to the fucking bone for peanuts, who can be exploited at will because they can't call the government to enforce labor regs. That creates a situation for employers that they can hire these people by the thousands, treat them like dirt, pay them barely anything, have them work in horrible conditions, and then basically toss them on the street. That situation is bad for everybody. It's certainly bad for Americans because if those exploitable people are available as labor why wouldn't an employer hire them rather than an American who will demand higher wages and better working conditions?
Ending that system of exploitation will suck, it will be a painful process that will destabilize food and labor markets. And knowing Trump, I'm quite sure there will be a lot of civil rights abuses, which I am strongly against. Everybody deserves to be treated with humanity and respect, including undocumented people who are being deported. But I also think that before we dive 100% into saying the whole thing is a bad idea, we should consider potential long-term effects. And if the result over the entire American labor market is there is no longer a cheap exploitable under-class, I think that's a good thing for everybody.
Funny thing is this could be done way more cheaply and humanely.
Have an amnesty. If you're in the country illegally, turn yourself in. You get $250 cash and a free ticket to wherever you came from.
Promise that'll cost less than arresting everyone and jailing them.