Ahh the joys of single parenting -- what an adventure I have to look forward to for the next 18 years!
To answer the OP, NO the non-custodial parent should not be credited; many valid arguements for this have already been put forward, so I'll not beat a dead horse. It's simply a case of a few bad apples spoiling the bushel.
Here in MT, if the custodial parent is on public assistance and a support order is being enforced, the state takes their share of the support to reimburse their coffers for the cost of assistance, and the custodial parent gets whatever's left over (in a nutshell, not totally clear on the particulars of their formulae). Good incentive, to my mind, for that parent to get on with making a better life and getting OFF welfare, so they have more sayso in how to use the support money.
I for one, as a custodial parent, do not have the time or the inclination to account for how I
money to support OUR child, nor should I have to; I am certain it would far outweigh any amt of support ordered to me by the court, which would likely result in an increase
in the support awarded, not a decrease.
In an ideal world yes, both parents would be in it for the good of the child. But for every parent who misuses support money for their own luxuries before seeing to their child's needs, there is a parent who is ducking paying any support in the first place by any means necessary. It's a two-way street. And the best way to avoid any fraud in the first place is for the parents to behave as ADULTS and see to the best interest of the child they both created. I know plenty of two-parent households that blow it on that count.