There's no specific reason why you need to get the 3 parts from Regis before you can interact with the Music Box. You can actually interact with the Music Box before getting any parts from the Regis.
Here's a breakdown of the situation:
* The Music Box is a key item that unlocks the Zero Zone in Area Zero, allowing you to access the final boss.
* You need 3 parts from the Regis to open the entrance to the Zero Zone, but they are not related to the Music Box.
* The Music Box itself is found in a chest at the location where the last Regis is defeated (in a very specific spot).
So, while getting the Regis parts is crucial to accessing the Zero Zone, it's not directly related to the Music Box. The Music Box is a separate item you need to unlock the final boss encounter.