The cynic in me wonders how many of the illegals would willingly become good tax-paying citizens when they get so many of the benefits now without having to bother with the paying.

The realist in me loves your plan, though, as long as we clamp down on the people who don't willingly sign up to be processed after we say we're opening up. It's about the only solution[1] that doesn't involve massive people round-ups and a giant wall, and the massive people round-ups would find ways to go horrifyingly wrong.

[1] Defined here as something actually changing from the horrible status quo, or, as I like to put it, "being solved".