You can specify who gets the deduction in your support order. I have 2 children and am the NCP (they're with me about 40% of the time). I get one deduction and my ex gets the other.
I think it should be based on your relative support amounts in the cs worksheets. For example, if one parent's contribution is calculated as 90% and the other as 10%, it would make sense that the 90% would get the deduction. In reality, I don't think a court (at least in WA state) would order more than half of the child deductions to a NCP (usually the father).
The official rationale I've heard is that people have to pay after tax when they take care of their children, so that it why it isn't tax deductible. The frustrating thing is that if kills you on your DTI if you pay it when applying for a mortgage and a parent can use it as income when they're receiving it and applying for a loan. So it's kind of the best of both worlds for a parent receiving it and horrible for the parent paying it. All I'd suggest is don't ever get behind. I've always paid mine on time. That's actually what screwed up my credit 'cause I when I was strapped for cash, I neglected my bills instead of CS.