It's never been clear to me that Qui Gonn would have done a better job than Obi Wan. It's Qui Gonn, after all, that rescues Anakin while leaving his mother in slavery and it is her eventual death is one of Anakin's biggest steps towards the dark side. Was Qui Gonn going to come back and free Schmi so Anakin wouldn't worry about her? I don't think so. Would Qui Gonn have stopped Anakin from being obsessive about Padme? I don't think so.
If someone needs blame, it's the council for entrusting Anakin to a very new Jedi Knight. But the council does it again when it entrusts Ahsoka to Anakin...