There are plenty of people the administration is trying to deport who neither entered nor remained in the country illegally.
For example, Rumeysa Ozturk who was arrested for engaging in 1st Amendment protected speech and put into deportation proceedings despite entering the country legally, staying in the country legally, and breaking none of our country's laws.
Do you think that such a deportation would make the US more or less appealing for immigration? After all, every immigrant has to suspect that they might become a target of such an enforcement action as well.