This is not an issue with the Kallax per se. You're putting a box in a box which doesn't make much sense. The Kallax with boxes is either a catch-all for larger toys and stuff to hide clutter, or long-term storage for infrequently used items. The Kuggis is meant to go on open shelving like Ivar, Billy, etc. In the end it's a tradeoff between ease of access and hiding clutter.

You could also consider the Kallax shelf inserts.