Your argument works for teenagers, because some of them are indeed mature, and have full awareness of what they're doing, as well as the potential consequences and repercussions. I certainly won't say that it's fair to say that there should be a clause where "underage girls with full knowledge of the law can be prosecuted", nor that determination of "full knowledge of the law" a simple matter in the first place. When you take the age down to something like 8, it may be more apparent why the law is there. It's easier to understand the concept of the line being drawn at 16 for statutory rape I suppose, now extend that to involvement of benefits of any form - and it's not hard to see why the law also wishes to push the age upwards for such cases. Certainly propositioning a minor to engage in sexual acts with returns/benefits/carrots of some form being involved requires the minor to have a higher degree of maturity to reject the proposition. Whether age equates to maturity is always a very debateable issue but one can only apply a rough guide in such cases, and age is a good enough proxy for most people.
Just my thoughts on the issue, cheers.