Just because someone has had personal issues and negative reactions throughout his career doesn't mean they can't turn things around.
I'm siding with RVDgurl & Shocky with things they've said, and adding a bit extra on why.
First; RVDgurl tagged the "the ___ are shit" phrase and it stands to reason. Why would anyone want to play for a worthless team? KC had a ton of upside coming into the season. They had quality WRs, a young and growing Defense, and best yet they were signing a QB who was the fill-in for Tom Brady and basically did what few others have.. made people feel easy that Brady was out.
Bottom line, with all that.. unfortunately, the Chiefs are still every bit what they've always been for the previous few years.. .. whether you wanna hear it or not.. .. shit. So tell me why Larry Johnson, who doesn't have many more miles in the tank, would want to continue drowning for a team that isn't trying to get him more involved - when he's proven that at times he can be great, when surrounded by a supporting cast??
Second; Shocky hit the nail on the head. Low risk, High reward. The Bengals didn't pick up any contract. They didn't offer a fortune. They didn't even guarantee Johnson anything. (to my knowledge) But the one thing they are GIVING HIM, that the Chiefs weren't.. was the opportunity to re-write his career and personal life. They're giving him a chance, an opportunity, to join a team that as it stands.. is 2nd best (through standings) in the AFC right now. (yes, 2nd best) They're giving him the ability to finally join a roster, a team, that can give him a supporting cast.
And if he fills in for Benson, (who re-wrote his personal life and career by joining the Bengals) and does a great job, then who's to say come next season we don't see the Bengals doing what almost every other team has done.. and add a RB by committee duo.
So, my personal take on the situation is that this isn't a stupid move.. its a great move. The Bengals aren't going to "go down" if Johnson brings his personal bullshit to Cincy with him. They're going to cut their losses and chalk it up as no harm, no foul - but at least it was worth the shot. Johnson isn't going to come in and separate the locker room, or take over the team. Hes going to come in, sit down, shut up, be a back-up, and prove himself. (all over again)