I find myself spending more time on my dirt bike than my street bike these days. But I won't give up either. Fortunately, it isn't parents that I have to worry about, it's the wife, but she bought me my KX250.
If it helps, the FZ6 (and several similar bikes) isn't a crotch rocket, it falls under the JSM category, and is probably better suited for someone in the age range that needs parental permission. Actually, the Ninja 250 would probably be the best choice for a beginning street rider under 20. To aid the argument, 70 mpg est. with a top speed around 80mph. A buddy of mine recently bought one as his first bike, and I was surprised by the power it has.