To be fair Runeterra isn't exactly a happy place
We have a kingdom that went from perfect sanctuary to hell on earth, so any champion who comes from that place will have some darkness to the pass.

We have another kingdom which is basically a more dark and sinister sparta with some secret spy mage order, aka noxus, so you can expect them to be war hungry, or dark edge lords

We have another kingdom that was completely ruined by said kingdom, with citizens whose lives were forever changed by war.

THAN WE HAVE ONE KINGDOM WITH A TRIBE OF PEOPLE WHO LIVE ONTOP OF A FREAKEN MOUTNAIN DEDICATED TO WAR which was also filled with racist biggots who kill you if you don't worship the sun

So what is the league world? it's a planet consumed with war and destruction, so is it really such a surprise that most the champions have sad pasts?
Hell, what are they called? Champions, not heroes, CHAMPIONS
Champions are people who were tested with hardship and saddening pasts but were able to over come it to become a inspiration to those around them, a champion.