I wouldn't say that I would not be as happy if we were to sign Correa, but I would be more nervous. In addition to oblong's legitimate concern about carrying his dead weight for the last several years of a 10+-year contract, he has also missed a month or more of games due to injuries on at least four separate occasions during his career. I don't think we know for sure that he is out of those woods.
Sure, there's no guarantee Baez or Story, or any player for that matter, won't miss big chunks of seasons due to injury, but the difference is they have no established history of that, and Correa does.
We can sign Correa, but we can't say we weren't warned.