Oh, I think that is such an excellent question! To be defamed by a man that you trusted in a public setting, to have him show no remorse at your supposed "death" until you were proved innocent of your crime... who would want him for the long run?
Consider the time period, however. A women's reputation was all that she had. She could not own property or act of her own free will, so she had to safeguard her reputation to make sure that she was not put out by her family and friends. This is what her father Leonato says upon Hero being accused:
why, she, O, she is fallen(145)
Into a pit of ink, that the wide sea
Hath drops too few to wash her clean again,
And salt too little which may season give
To her foul tainted flesh!
He claims at this point that she is as good as dead to him, for in losing her reputation, his own reputation has been tainted as well. This is why the death scheme is enacted, to give some hope that Hero might be exonerated.
The only way for her to be clearly and definitively declared innocent, however, is for Claudius to accept her as his wife. If, in the end, she had not married him, then she would be supposed to still be tainted. She has to be wed to him, as was originally planned, if she hopes to regain her full reputation.