Here's what rhymes with unaccountable.

Consider these alternatives

apolitical / critical unelected / rejected undemocratic / democratic amoral / moral unrepresentative / representative unfeeling / feeling inscrutable / suitable overreaching / teaching dictatorial / editorial unmanageable / manageable unwarranted / warranted inefficient / sufficient powerless / flowerless comically / chronically unwise / size omnipresent / present ineffectual / intellectual unfathomable / fashionable underappreciated / dated unregulated / related untrained / obtained unsympathetic / magnetic despotic / logic