They need a candidate who can be taken seriously. I doubt Biden can fill the bill (so to speak).
Is Chelsea old enough? Hmm... yes she is (35) but she does she have a political track record? Can she be blackmailed? (yes to the second but no to the first, which IMHO tends to disqualify her)
Even the media - even the drive-by media couldn’t possibly take Michelle or Chelsea seriously. I mean really? I know that the media is lower than flesh-eating bacteria, but could they really swallow Michelle or Chelsea ?