Here's why:
* Trap Zone: The Trap Zone is a designated area on your field where you place Trap Cards. You can only have a maximum of 5 Trap Cards in your Trap Zone at any given time.
* Quick-Play Spell Cards: Quick-Play Spell Cards can be activated during either your Main Phase or your opponent's Main Phase, but they are not placed in the Trap Zone. They are activated directly from your hand and resolve immediately.
Therefore, having a full Trap Zone does not prevent you from activating Quick-Play Spell Cards. You are only limited by the number of Trap Cards in your Trap Zone.