>not understanding the reason for this
Protip: if you are out of box space, you can use the WiFi system as a box by making impossible requests.
How to fix:
1) Run a legality checker on every single pokemon submitted and requested in trades. If a request is invalid, don't let the user make it. If the uploaded mon is invalid, "confiscate" it and ban the user from Nintendo WFC for a month.
2) let a player blacklist any trader they don't like. The first person you see offering a Bidoof for an Arceus, you hit "hide this user" and no more of his trades will appear in the GTS, nor will he ever battle you in Wifi Random Matchups. He is gone from your pokemon world forever.
3) Let players use WFC for "Cloud Boxes" so there's less motive to do this stupid shit, or just make the box limit 99 boxes.