My response:
Well, there are no "national" laws. Child support is a "State" issue, and such laws are different from one State to the next. So, as the old saying goes, "One size [does not] fit all."
However, in California, while child support is for the "benefit" of the minor child, the child, either during or after minority, does not have "legal standing" to sue for support arrearages. Remember, the issue of child support is either an agreement between both parents and signed by the judge, or it's a mandatory guideline amount ordered to be paid by the NCP to the CP for the "benefit" of the minor child(ren). [See Marriage of Comer, 14 Cal.4th at 510, 516, 59 Cal.Rptr.2d at 156, 160, and Marriage of Dancy, 82 Cal.App.4th at 1156-1157, 98 Cal.Rptr.2d at 785]
Although a child support obligation runs to the supported children and not the custodial parent, the children generally are not the "real parties in interest" in an execution (or other) action to enforce child support arrearages--i.e., the parent obligee (or the local child support agency on the custodial parent's behalf) is the real party in interest with standing to enforce the order and collect the arrearages. [Marriage of Utigard (1981) 126 Cal.App.3d 133, 143, 178 Cal.Rptr. 546, 551; see also County of Shasta v. Smith (1995) 38 Cal.App.4th 329, 335, 45 Cal.Rptr.2d 52, 55--"custodial parent, not the child, has the beneficial interest in collecting arrearages in child support"]
The rationale is that an action for accrued child support is "presumed" to be one for reimbursement to the custodial parent. While the children are the direct beneficiaries of the underlying award, the custodial parent is the direct beneficiary (real party in interest) of an order securing arrearages. [Marriage of Utigard, supra, 126 Cal.App.3d at 143, 178 Cal.Rptr. at 551; County of Shasta v. Smith, supra, 38 Cal.App.4th at 335, 45 Cal.Rptr.2d at 55]
IAAL