Yes, this is, why Hawke a tragic hero.
A world-savig character why more interest?
I think you misunderstand.
I don't need a world-saving hero in order for a character to interest me. I welcome smaller, more personal plotlines, with more localized goals.
If taking care of family is Hawke's primary motive, then Hawke has completely failed by the middle of the second act. I don't much enjoy stories about characters who completely fail at their most cherished goals - at least not unless they gain something else in the process.
Losing Mom was not only foreshadowed, but the templar who'd been investigating the missing women turned the investigation over to Hawke in Act 1. Hawke did nothing about it. I found that immensely frustrating.
1. Warden: What motivated him/her? Surviving. S/He did not choose his/her fate: it happened.
That depends on the Warden. My dwarf commoner didn't give 2 hoots about saving the surfacers from the darkspawn. She accumulated quite a bit of coin, and once she'd secured a future for her mother and sister in Orzammar (by putting Bhelen on the throne), she ran off to join the Legion of the Dead. Never made it to the landsmeet.
A Cousland Warden gets to kill Howe, and a male Cousland can put himself on the throne with Anora.
Other Wardens I've played have had other motives - some personal, some were all about being the HoF.
2. Inquisitor: What motivated him/her? Surviving. S/He did not choose his/her fate: it happened.
I've not yet completed my first playthrough of DAI, so I'm not very well prepared to discuss it. I do think that different Inkys can have different motives, though, especially since you deal with a lot of different factions in that game. Some Inkys might be wanting to take over the world, while others might just want to move on once the breaches are closed and Cory defeated.
One thing I like about DAI is the way that the 3 advisors represent 3 uniquely different ways to solve a problem: via diplomacy, force, or subterfuge. How you use the advisors can say a lot about Inky.
And I do not want to convinve you (about the tastes silly to argue) I just wote the my opinion.
That's cool - you really can't convince somebody to like something they really don't especially like.
That's not to say that there aren't some things about DA2 that I really do like - it's just that Hawke isn't one of them.