TGAA's blood curse at the end of case 1 is actually the funniest thing in the series. "Okay this is a prequel but we're not going to have any hard continuity to the main series, only oblique references here and there- OH EXCEPT PHOENIX'S FAMILY AND THE PAYNES HAVE BEEN BEEFING FOR OVER A HUNDRED YEARS. YEAH IT WAS SO BAD KAZUMA MADE A SACRED VOW ABOUT IT." He specifically curses Auchi, not on his own behalf, but for Naruhodo's lineage. Doesn't even have to be biologically related! Susato pretends to be related to Ryuunosuke in game 2 and that is thematically recognized as fulfilling the requirements of Kazuma's vow in the first game. A century and a whole country away, Apollo has the narrative weight to beat a Payne, and he is Phoenix's adopted daughter's half-brother. This family literally goes to a whole other country to escape the Naruhodo clan, and still can't shake them. Twice.
I 100% choose to believe that since magic is real in the aa universe Kazuma managed to actually curse an entire bloodline. He has no idea the far reaching consequences of this. He did this accidentally through the sheer power of Gay Love and A Really Cool Sword.