To put it bluntly, Nao has more in common with Tomoya from Clannad than Tomoyo. She isn’t being treated in the same respect as a heroine in Key works, or many works, normally is, she’s being treated far more like you’d expect from a protag. You’re looking merely at the superficial label of delinquent, not at how the character is being framed.
To put it even more bluntly, Nao is written more like a person, than like a archetype. She’s neither tied down completely in her past nor completely juxtaposed with it. She doesn’t have that ‘Key weakness that needs to be fulfilled by the protag’, or at least not yet, nor is she being shown as this collection of strong traits to be torn down later.
Blegh. All I’ve done here is repeat my stress of she’s being treated more like how Key has treated protags than how they’ve treated heroines. If you don’t even understand that’s a difference to begin with, I can’t really do much more to help you.