No, having a Dad isn't normality, it's brainwashing propaganda.
You're inferring that any family setup that doesn't include a Dad is therefore abnormal.
What's normal is being raised by parents (however many) who love, cherish, respect their children, raise them to have manners and morals and respect for other people, who work hard in life and have a strong work ethic, etc.
I'm a single parent (not by choice) and my children are quite happy, thanks. We've moved away from where we used to live and they love where we are now, they get to see their grandparents several times a week, they're all doing brilliantly well in their new schools - DS is happier than he has been in years actually.
Oh and funnily enough, guess who put in the vast majority of the work raising the three of them until my ex decided he wanted out? Clue: it wasn't him. Guess who's now doing it all. Clue again: it's still not him.
He was rarely there. His friends and family were always more important and demanding of his time than we ever were. We were a burden - he only realises how much he loves the kids now that they're not there. He wasn't a great role model either - DS was a constant disappointment as he wasn't into football and is highly strung (a 'tart', to use ex's lovely description) so used to get upset a lot.
The kids aren't crying for Dad. We've had a couple of tearful episodes, but really they're quite happy as they are. They now have my Dad as a strong role model, who loves them for who they are, rather than who he wants them to be, and my two brothers, who are both weird and wonderful and eccentric, providing strong male characters who do things their way, regardless of what society thinks.
So, exactly why is my ex more important to my dc than the other male role models who show their appreciation for my dc being the great little individuals they are? Is it better that they have a Dad around just for the sake of it, a Dad who really isn't all that interested, who wants to mold his sons into football-loving, misogynistic (the tales I could tell!), pissheads like pretty much all the men in his family? Or are my dc better off with men around who love them exactly as they are and boost their confidence and self-esteem every single day?
I know what I'd choose.