We don't have any synonyms for why-not yet.
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Definition of why-not:
(adv) :
(interrogative) For what cause, reason, or purpose.
(adv) :
Introducing a complete question.
(n) :
Reason.
(v) :
(intransitive, transitive) To ask (someone) the question "why?".
(adv) :
With a negative, used rhetorically to make a suggestion.
(adv) :
(relative) For which cause, reason, or purpose.