Could you explain why Elizabeth doesnt beg John to 'confess' at the end of the play and what does she see as John's 'goodness'?

Elizabeth does not beg John to confess because of what she
refers to as "his goodness".  She sees that he refuses to be a hypocrite and a liar.  He
has denounced the witch trials as a farce and for him to now sign his name to a false
declaration of guilt would be hypocritical.  He will not implicate other innocent lives
to save his own life, even if it means leaving his children without a father.  John
Proctor had had an affair briefly with Abigail.  He had dishonored his name by doing
that, but by refusing to save his own life through lying, Elizabeth declares that John
now has back his "goodness", or his good name and his honor.