I don't see why people are focusing on the number of people the OP's friend has slept with. How on earth is that relevant?
The question of different fathers is relevant only in terms of how it directly affects the children. I don't see how anyone can put a positive spin on children having to experience all the insecurity and unpleasantness that go with the vast majority of relationship breakdowns. No one would deliberately put a child through that once, let alone repeatedly. If they did then they would be a bad parent.
Yet it happens. Sometimes for unforseeable reasons, sometimes for slightly more obvious but very complex ones.
IMO, assuming that you want a normative heterosexual live-in relationship, it is important to get to know someone before deciding to introduce them to your DC, let alone have another child with them. As soon as you introduce a new partner, you are creating a bond between that person and your child that could prove devastating if broken.
That's why although accidents happen in new relationships and sometimes work out very well, normally it's not a great idea to get pregnant with a man you've only known 6 months, for example. Not only is the conceived child at a higher risk of being left fatherless if you subsequently discover the father is an abusive wanker, but so is the child you already have who has already witnessed the fallout from one relationship breakdown.
However, accidents happen. Sometimes pregnancies happen deliberately because hope and love are powerful motivating factors and it's very difficult to believe the worst of someone you are in love with. There are all sorts of reasons. I don't think many mothers would consciously choose to be reckless about it.
From what the OP has said about her friend though, the 4x4 moniker is undeserved, since although there are four fathers, the number of relationship breakdowns is two, which is much more common.
I know a number of women who have children whose fathers aren't around. The most stable ones are the ones who never had the father around in the home in the first place, since the children have been spared the fallout of the crumbling relationship and everything that goes with it. You could argue that the best mothers shouldn't live with the father of their DC's at all, since this exposes the children to far less risk. 