Being a former Examiner for the American Board of Plastic Surgery, examining candidates for several years who wanted to become Board Certified, I can tell you that I can't imagine any reason why somebody who had performed the years of necessary training and education would not try to complete their Board Certification which is the gold standard in plastic surgery qualifications. However, please understand that it is no easy task to pass the boards though, requiring the blessing of the program director who trained you, the passing of an extensive written examination, and culminating in a rigorous oral exam on your own work plus challenging cases presented to the candidate by the Board examiners. Even one's ethics and billing practices are put under scrutiny.
So, when a person has all the training to be Board Certified but isn't you have to wonder a bit about them. I would estimate that it is usually because they have failed to pass the exams either at the written stage, the oral exam stage, or even possibly the Board doesn't feel they are ethical enough to be blessed as Board Certified.
The fundamental job of the Board is to determine that those who are Certified are safe and ethical plastic surgeons whom you can trust with your care. Their talent as surgeons and whether they are the right one for you is still up to your discretion and research as these are not the job of the Board.