I appreciate you taking the time to share your thoughts! While making the tear a quick action does impact the Banshee's action economy, the tear no longer closes unless the Banshee chooses to close it, so it taxes the first turn, but generally only that turn.
Making the core a quick action synergized well with the Banshee's use of Ordnance weapons, using its first action to attack and the following action to pop the core. Making it a quick action also allowed the core to as powerful as it is (repeated use, guaranteed damage, teleporting) due to it carrying risk and action cost. While making it a reaction wouldn't be unreasonable, it would likely require nerfing the effects. I want cores to feel like powerful and important choices, and making the player consider how to use it in the action economy is a part of that.