So, allow me to show you something.
Wakka's parent - killed by Sin when Wakka was a kid
Role in FFX - motivate Wakka to banish Sin
Tidus' parent - Father -Braska's guardian and Final Aeon / Mother - died soon after his husband dissappear.
Role in FFX - For the effect of a plot twist and appear as the final boss
Yuna's parent - Father -The high summoner that once defeated Sin.
Mother - An Al Bhed
Role in FFX - Motivate Yuna to follow his father's footsteps and also as a half Al Bhed summoner might inflict problems.
Rikku's parent - Father - The guy that lend you his airship
Role in FFX - Allow you to get inside Sin.
The parents of the characters that get mentioned did play a specific and rather important role in the game itself but maybe not Wakka since it focus more on his brother than his parents.
We had no idea who Kimahri, Lulu nor Auron parents are because Square did not intend any major role which reflect on the parentage of these specific characters.
So, the role intended for Paine in FFX-2 by Square is mainly of her past with the crimson squad. Her parentage doesn't play any important role in the game so Square won't bother to said much about it either unless her parentage had something to do with the plot which Square didn't intended it to.