Bilbo Baggins, arguably the greatest protagonist that ever "lived", had a normal healthy family. Both his parents (Bungo Baggins and Belladona Took) died of old age as they crept on a century of life. Healthy families CAN make good heroes!
He...started adventuring pretty late I'd say. I don't remember him leaving Shire with dwarves saying "bye mom, I'll be back in few years, just let me take a walk to mountain and talk to the dragon". And I'd not call him greatest protagonist, to be honest.
Because main part of journey falls on his nephew...and his parents drawned. So - Tolkien also used tropes and archetypes, and was HELL GOOD at it. And it's nothing wrong about them, actually. As long as they are used well.
As for parents... I honestly prefer "blank" characters, because I like to imagine things myself both prior and after game timespan. "preset" family brings some limits. If we remember Shepard - only one of them had alive mother. And mine was "earthborn" - full headcanon freedom.
Hawke puzzled me at first, because family was not only preset but also alive (well...most of family...most of time..). But after several PTs I found that it does not bother me that much (as I first thought it will). Characters left enough freedom to build my own version of family relations, I could headcanon detailes and events.
Thouh, probably, Leandra could have say a word or two in game about relations with an apostate..