Because he does not need to. He mainly needs it on his arms and legs, so that he has increased tensile strength there in order to make use of that fist/feet retract mechanic. He's obviously trying to use the least amount of haki he needs to, so that the time limit isn't getting any smaller than it already is.
And if they try to slice him up, he will try to block it with his swords, like he always does.
And I did not assume anything. It's obviously just very very uneconomic if he randomly has half his body covered in haki, cause we know for a fact that using this much haki for a prolonged period of time has a very short time limit. So if this "leak" is true, that "half body haki"- thing most likely is the drawback of whatever he's aiming for with that.
And I just doubt that this stuff is going to happen and that it's a legit leak. We can agree to disagree on that.