FFS. Could you puruse the stereotypes any further?!
Plenty - and I would hazard a guess most - single mums bring up their children without police involvement, where their children achieve their academic potential and attend 6th form and then university. 2 out of 3 of mine are in/went to university and I've been single for 16 years with minimal involvement from their dad. The other is doing a trade apprenticeship and will out earn the rest of us, I suspect, within about 5 years. Most of us raise children who are polite, decent human beings with good values. Indeed, when they have seen their mother struggle, they have a good understanding of the value of money and what is needed to survive. I've worked full time for most of those 16 years, with seasonal and ad-hoc work on the side. Their father hasn't paid a penny. They all have a good work ethic, having worked since they were 16.
As for most single mums not staying single. Well, in my circles, those of who are single have remained that way. I'm no nun, but I have managed to separate my children's lives from my own emotional wants and needs. They haven't had men around at all - in fact, a recent dinner when a male colleague of mine came over to discuss some work stuff, my eldest's hackles were raised to such an extent that I feel I perhaps did the wrong thing. He is now struggling to accept that now they are no longer children, I will be pursuing my own life. He gets it on an intellectual level but admits he doesn't really like it.
If you pursue the single mum stereotype, sure, there'll be plenty of people who fulfill it. Don't forget many of us don't. And also don't forget that plenty of children in together families struggle, go off the rails, are rude, are involved with the police and don't reach their academic potentials. Why aren't you talking about them in such negative terms?