Also, we have a very long and rich history of acts to legalize illegals, frequently very specific ones. Just look through the congressional records of a half century or a century ago -- "An act for the relief of . . . " There are thousands.
Passing sensible, restrictionist, laws now will be a lot easier without it seeming (as your post does) that we want to re-fight, and illegalize people who became legal by act of Congress.
Review the ratification history of the 14th Amendment.
You may not like the 1986 law, but it's the law..
Is it?
Not by US v Wong Kim Ark or Plyer v Doe and certainly not according to the opinions expressed in the first case before the SCOTUS after ratification.