My point isn't to insult, just to point out that if they're willing to pay for insurance, they're willing to pay. To coerce the girl to change residences for money does not send a good message.
I don't think insurance is a necessity (as do all of us here), and funds should definitely be contributed by the minor child to fund their privilege.
But keep in mind, while everyone is talking about child support covering the necessities in life, insurance is NOT necessarily a necessity, which means it technically falls under the "extra" category. Which means a CP can ask for help, but the NCP is not under the obligation to oblige. In this case, if the NCP is willing to contribute to insurance, they should just go ahead and do it. For goodness sake, the NCP can shop the insurance themselves and stipulate the policy (and driving stipulations for the daughter) if they want to.