Imo it depends on the setting.
When it comes to your standard Pokemon journey story, a modern setting, etc., it seems very dramatic and a little overdone for the character to have been, idk, the sole survivor of a serial killer's rampage that destroyed his family and his childhood sweetheart, or something, you know? That doesn't mean they can't have experienced smaller struggles, but typically they're things that are more standard-- grew apart from the family, cut ties with a sibling, feel stifled by the family's constant overbearing rules, etc.
That said, I have written in a setting where my characters were born and shaped by a really vicious, awful war, and those backstories were often darker. Had a character (nice, little bit lazy, charming dude) who had tortured prisoners; had a character who was bribed to murder his ex and proceeded to a few more people before shifting gears and ending up in a perfectly normal, if not very happy, relationship, etc. The difference is that in these cases, that kind of backstory is normal; it's weird if they haven't been hit by even a little spillover from the devastation of the war, so. SHRUGS.