When doing the "only equipment which has drawbacks" quests, equipment withWeak Strike isn't letting me proceed. Aside: it'd be nice if prohibited equipment could glow red on the equip screen for these quests, and likewise only equipment with drawbacks would show up when "usable" is checked.
I don't think it's a bug that Weak Strike doesn't count as a drawback card. But I do think that the equipment screen should definitely show the red glow for items that don't qualify for that quest challenge, and the 'usable' filter should be changed to filter out all items which don't qualify for the quest. Meanwhile though, a helpful workaround is to type 'handicap' into the item search box. That will only show items which qualify for the 'only equipment which have drawbacks' quest.
Try to to confuse card quality with the card function. Weak Strike's quality is Bad (black title bar), but it's type is Attack (red background). Drawback cards have a black background to indicate their type. I'm 99.9% sure that they all have Bad for their quality as well, but that's a completely separate piece of information. See here for more info on the parts of a card.
Raging Strike is a bronze quality ('average') drawback card. And Blind Rage is paper quality ('weak'). So there are some that aren't 'bad'.