Is it important to be able to successfully portray both a Face AND a Heel?

Is it important for wrestlers to be able to successfully and believably portray both a face and a heel character? Or can they still prosper by playing a good/bad guy for most of their career?
What if they aren't entertaining as a face - should they become a heel (and vice versa)?

Do you think Tweeners (both a face and heel, sometimes an anti-hero) are important?

Thanks.