Single mother of two sons here. Interesting about male role models. I've been pretty strongly influenced by advice that boys without strong male role models (doesn't have to be a dad) tend to have worse outcomes and be less happy as they grow up. Like all nature/nurture stuff you can theorise about why this might be the case, but my understanding (ten years ago when I split up with their dad) was that the correlation was pretty strong, so I always bent over backwards to stay on good terms with their dad so that they could see him freely and often. They're very close to my dad too.
They definitely have a very very different relationship with their dad to the one they have with me - much more banter , more piss-taking, less earnest stuff about A Level choices. They talk to him more freely if they're having girlfriend trouble. Plus lots of rough-housing and football with my dad when they were little, which is stuff I'd never have done (and their dad wasn't particularly inclined towards either).
I think the benefit of having more than one close role model is partly about just seeing different ways to be? And also, realistically, past the age of three or so most kids start to strongly identify as male or female and start looking for examples of how adults of that sex conduct themselves. If that role model isn't someone who loves them and prioritises their best interests, it can be pretty problematic I'd guess.
All that said, 'handing them over' at 11 is hooey, obviously (and I wonder whether Biddulph himself took responsibility for all the GP, dentist and teacher appointments, world book day costumes, presents for birthday parties, shoe-fittings, play dates, eye tests, inset day childcare, sick day childcare, nit combing and school trip packed lunches... or does 'handing over' only apply to the fun stuff?)