I don't have a horse in this race, but I do have a question. If you don't deport illegal immigrants, why not just open the border to everyone to come in? (let's ignore criminal records, etc for this exercise). What's the point of not letting people in but then if they manage to come in illegally, assume it's all good and they can stay?

That's the question, isn't it? Why not just do that? Who are you trying to keep out of the country, and for what end, and is that end best attained by removing people from the country who aren't the ones you are trying to keep out?

For instance, if you believe the border should be strict to keep out serial killers, what does that have to do with removing Korean car factory workers who aren't serial killers?

No horse either but here is an attempt (ignoring criminal record as you say): Opening the border and letting her rip is clearly not sustainable in the medium term. So you try to make it (reasonably) hard to get in incl. turning people away at the border.

Once they are in (incl illegally so) you concede you have lost on this instance. Now you admit that forcefully removing immigrants carries too high a cost (literally + damage in the communities you remove the immigrants from + your humanitarian image). So you don't.

Somehow that balance seems really hard to get right and edge cases (criminal record) matter.

Because we like second-class citizens because its easier to exploit their labor.

Buying into the narrative that any of this is about illegal immigrants is a red herring. Immigration is merely a pretext for enabling an unaccountable fascist police state using big data from the consumer surveillance industry to both keep enough people believing the regime's abject reality-insulting lies (the carrot), while extralegally punishing anybody who might be too effective at speaking out (the stick). This is painfully obvious as they move on to target US citizens - both the boots on the ground terror gangs, as well as the increasing political rhetoric about deporting citizens.