Well...in reality, the backstory is a plot device that you don't HAVE to bring up unless it is pertinent in the overall narrative going forward.
If your characters act a certain way and are questioned on it, you can have them explain it and present challenge or acceptance based on that interaction but...nobody said you HAD to say anything about it.
Now, if something central to the plot happened in the backstory IE: Batman ultimately BECAME Batman because of the injustice he faced at the hand of a criminal/failing of law enforcement/vengeance, then yeah. Now we're telling a coming of age story or origin story or something where, yeah, the events of the past have more merit on the future.
But...you first need to figure out what sort of story you're telling.
Are we character driven, plot driven, setting driven? Are you character's internal angst stemming from the nature vs. nurture trope? Do your characters treat other people like crap because THEY were treated like crap? (vicious cycle?) Can your plot be adjusted and will the outcome be the same?
Do some "What if" exercises; take your characters through some plot points like: How much would character A change if I said their parents DIDN'T abuse them?
What would happen if character B did this instead of what I originally intended?
And yeah, I agree with everyone else, here. Cliche is a moment in the story when you find yourself rolling your eyes. A character can have a tragic backstory in lots of different stories out there and I promise, the ones you DIDN'T notice are not the problem stories.
I'll just say: tell the story you want to tell. If you characters need all of that challenge in their backstory to temper them for whatever they are about to face, then so be it but if it's there "just because" then, yeah, you're gonna have a problem.