I don't see anyway that it will be believable that if you off someone there family member will still even talk to you let alone give you a quest. Especially If that scenario happens a lot where a family member steps in and will still give you a quest it will be broken.
Yeah. It's good because it avoids the conundrum between accidentally killing quest givers or dealing with essential characters ; but they'll have to throw in a mighty amount of persuasion to make it work.
Maybe something different each time ? Like, figuring out for each NPC what will get them to talk to you - finding out a secret and blackmailing, holding someone/something hostage, bribery, false remorse, framing someone else, finding some artifact for them, etc.