There's nothing wrong with flashbacks in video games or any other form of story telling medium. As others have said, it's about telling a story effectively. It doesn't matter how you do it so long as you do it well.
I pretty much made my point by now, but I ranted a bit for the rest of this post but felt like leaving it in anyway.
Also, here's how absurd the idea of no flashbacks is: Try to live the next week without telling somebody a story about your past. That is, a story about anything that happened prior to today. It's like you just began an RPG starring yourself and today is the starting point.
Pretty much the only time no flashbacks works is when you're playing a blank slate character or a character whose life has been so incredibly dull and average thus far that it needs no explaining. I suppose they could be completely one dimensional too.
You know, gamers complain so much how games need better stories, but they for the most part seem to have a middle school level (maybe high school level) of understanding of what makes good stories. Which is fine if that's your thing, but there are LOTS of kinds of stories. For example, characters don't have to grow. Simply observing them is sufficient provided their actions are remarkable.