>>55825417They only stay in the past because of gameplay purposes, you fucking idiot. If Arceus said "wow you did it, great job! you can go home now :D" and sent the protagonist back, then the game would reach a definitive end-state that would require you to start a new save file, and more importantly, lock you out of being able to use or transfer your Pokemon.
BDSP makes it clear that Lucas/Dawn DOES return to their time in spite of this gameplay distinction, and when they do, they're greeted with the Azure Flute having mysteriously appeared in their bedroom, which allows them to once again commune with, battle, capture and command a fraction of God in their present time.