It's hardly as straightforward as that though, is it?
Ok there may on the face of it be a tax benefit to the payer, a marginal rate deduction. But it puts a burden on the recipient that wouldn't be there if the money is classified as being maintenance for kids. This aggregate benefit also disappears if the income of the recipient changes in the future, pushing them into the high rate band (or if the tax bands, or tax rules for maintenance change).
Anyway, I presume maintenance for children is only until they reach adulthood. I'm not familiar with such agreements but if one agrees to diddle the numbers in favour of their ex, in order to get a tax benefit, couldn't they end up with a much larger bill in the long term, paying maintenance indefinitely..?