I think it's highly twee as a label, and very one-upmanship.
On a related note, I also find it depressing the amount of women I meet at professional events, conferences, work events, who, when first introduced, state their motherhood as the first thing about them, with their job as an almost throwaway nth place comment.
In that context, you are an auditor, solicitor, marketing director - whatever you do. Nobody gives a fuck about your kids at that point in time, and it really diminishes your professional stature. Mention the family over lunch as part of natural conversation, sure, but don't let it define you as you shake the hand of the person you are meeting for the first time.
(I have not met one man who has said "Hi, i'm Bob and I'm a father of 3 and blah blah blah....oh and I also run the HR team at Jones and co")