That would be nice but that's naive.

Until now, the EU has had no digital way to track immigration and register visitors like practically every other major developed country in the world (typical Europe, 15 years behind). All other major countries using biometrics (USA, China come to mind) still have an immigration officer handling foreign passport holders. Collecting fingerprints, verifying visas, purpose of visits, etc...... still better done with a human. EES just allows digital tracking. Otherwise with stamps, you could overstay and an officer could never notice if he/she didn't bother to match up the entry stamps, immigrants could commit crimes without fingerprints in the database, etc......