Andrew makes a good point.
How much of this money 'owed' is owed by dads who have children by multiple women? I'd be interested to know that statistic.
Also how many of those who owe money are unemployed?
My own suspicion is that if you are a low earning NRP, it is actually better for you to earn less/give up work and become a SAHP to any subsequent children with a new partner/ go self employed, work a few hours a week and top up your earnings with tax credits thereby minimising any maintenance liability.
I honestly think the more you impose conditions to try and recover monies owed, the more methods of avoidance you'll see. Not to say it won't be successful at least in part, but I think it is unlikely you will effect a complete sea change.
And of course you may also see an increased no of NRP's seeking 50/50 care, when often no maintenance will be payable...