Sure enough, I won't be able to use the second deck in the first runthrough of the first scenario...but I can use it in the second one. If we even want to abuse the rules I could kill my first player and the rules tell you to restart over. I could essentially make characters until I get exactly the weakness that I want
Or you could just pick the one you want. It's a cooperative game, after all, and I'm pretty sure the above approach would have the same "Yeah, dude, we're not going to play with you any more" response from anyone unfortunate enough to be stuck playing with you as outright cheating would.
Is there some ambiguity? Yes. But when you consider the player count descriptions and the instructions for starter decks, it's pretty clear how it's supposed to work. If you want to torment the rules to fit your personal preference, that's up to you, but don't pretend it's some honest pursuit of rule integrity, and don't expect many people to think you're anything but a rules lawyer on a rampage.
I don't think the rulebook was talking about how to make a deck that you then let sit around. It's about how you make one just before playing.
I think this exactly right. The Rules Reference says "During a campaign, players build a deck before playing the first scenario." A deck is intended to be for a campaign run. We don't know for sure how decks might transition from one campaign to another (I'm guessing they don't) but it looks to me like you'd redraw a new basic weakness even for the same deck starting a new campaign.