It depends on the situation. Lots of RP use it for themselves. Also, everyone would have to keep a hole whether they had children or not so to say it's all for the child and then on the other hand say it contributes towards housing and bills is somewhat contradictory.
RPs can also claim child benefit, universal credit and 85% of childcare back (if they're not high earners this is not all cases). In some situations RPs are only having the children one night more than the NRP who can't claim anything.
Generally the expectation is the NRP cannot claim anything, not entitled to housing, has to do all the pick ups and drop offs etc.
CMS however do fail both sides. Lots of RPs cannot get any maintenance from the NRP. They duck and dive, hide assets, go self employed, stop working. The Cms also hold money for long periods of time even though it's been taken from one parent and thus leaving the RP short.
I agree that everyone should pay for their kids but the disparity in the system is unbelievable. In this case, if the dad is paying maintenance I don't feel he should lose is inheritance. However if he's quit his job to avoid paying I can see the OPs point and don't think it's as grabby as it seems, if of course, the money would be spent on the kids entirely. Not a family holiday or offsetting life costs that everyone had (housing, bills, holidays, cars etc).