I agree with that --- but who said it's got to be all or nothing? Police ticket speeders they catch --- but they don't get all of them, murderers who are caught are put in prison, but some murderers run loose --- that doesn't mean we just don't catch any.
They should start with those committing serious crime like felony document fraud and that should be easy enough by cleaning out the Social Security number database and going after Identity theft --- that should gain them permanent deportation with no rights to visit here ever. Deport those illegals getting caught driving with no license and insurance, DWI's, shoplifting, gang membership, etc etc. End the practice of anchor babies, especially those whose mothers never intend to pay their hospital bill and also use their babies for welfare checks, foods stamps and the rest. Cut all that off. No more government freebies of any kind.
They won't catch 100% this way --- but they'll have gotten the very worst types out of here.