Immigration enforcement is literally the use of force to maintain a larger economic inequality than the downward pressure you referred to.
Not in some subtle way. Enforcing politically decided inequality is literally the purpose of ICE.
It makes people uncomfortable to talk of it in those terms, but when you get down to it, a lot of people want to see enforced inequality, and vote for it.
They couch in terms like "downward pressure" to abstract things away from the people's lived experience, to make it palatable to make one group of people worse off so that another group of people can be better off.
The economics abstraction has the added bonus that we avoid mentionining the lived reality: the perpetual fear, lack of humanity and so forth that come with, say, splitting up families, and preventing them from having any reasonable avenue for leaving an ordinary life. (I've known too many immigrants who cannot find a way to solve the bureaucracy problem, and cannot even determine their legal status, or in some cases if they did try to find out they risk being split from their own immediate family, so perpetual fear and avoidance of authority is their only realistic option for living.)