"immigration is ... necessary for continued growth and innovation."

Pure, utter hogwash.  All you've described is a Ponzi scheme, not a sustainable economic model.  Per capita economic growth doesn't depend one bit on population growth, whether from immigration or from births.

Even if your claim were true (which it isn't), what would you propose for the countries supplying immigrants?  The world's countries can't all experience positive net immigration all at once - for some to have positive net amounts of immigrants, others must have negative amounts.