So the box happens to have 13 locks.

And each lock represents every canonical game in the series.

To make more sense of this, let's assume that the locks only open once a certain event triggers it, and those events are what happens at the ending of each game.

So far, and without counting the remakes and the Back Cover movie, we have 12 games in the series which are canon and which have major events at the ending (UX and DR will definitely have one).

And what if the 13th game (which is probably the warm-up for KH4) is the game whose events at the ending opens the box?

If this is true, then that would mean the box plays a major role in KH4 (as expected) and narratively, it would explain why Nomura decided to include it

SpoilerShowin that post credits scene of KH3.

I believe it contains a Pandoras Box kind of thing. Like once it opens, chaos is unleashed and this would also be a major plotpoint in KH4 and beyond.