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.
Notably, deporting US citizens would also make the US less appealing for immigration. Would you agree with that? Since fewer people would want to travel to a country where even its own citizens are not safe living there.
Considering your other arguments above, I assume you are also volunteering to be one of the people deported from the EU for the sake of making it less appealing for immigration?
Of course it would make the US less appealing, which means the immigrants with the most optionality of where to go (like researchers, engineers, and high value contributors in general) are disproportionately likely to seek other destinations.
It would have the least deterrent force on those who are already criminal and otherwise lawless or desperate.
Back to your claim about this being an "effective" immigration policy: no it's not.