I come from a proverbial 'broken' home. Possibly I would have made different life choices had my father been present in my younger years (we're in contact now), however I deem this to be irrelevent when I realise it could've shaped my life to be so different to what it is now and I doubt I would have met my DH which doesn't bear thinking about.
That being said I wasn't without a 'father' figure per say, my maternal grandfather was a constant in our lives growing up and my older brother provided a male view when needed. I feel I messed up on my life and would used to blame my father for not being present, however now I realise it was my decision to take those routes and it as made me the person I am today.
To answer the question, Yes I do feel it is important to have a father figure in a child's life, though as so many have pointed it's not always best or indeed viable that the biological father be in their lives. DH is a great father to our daughter and I like to think if anything happens, he'll always be part of her and our other LO's lives.
I have to say I don't see men as the 'disciplinary' of the family. My mother never raised a hand to us, yet would scare us silly by threatening to and carrying out said threat of sending us to our room (we had no playstations or tellys even than!) Though has to be said DD takes more notice of DH when he tells her off than myself!
I agree also that having a relationship with 2 separated and happy parents is better than living in a house with 2 unhappily attached parents.