L has never used the Death Note, so seeing people cosplaying with it annoys me. But I suppose they have a reason for a doing it. My guess would be that he died in the process of testing the Death Note and that's why it's with him. Sounds weird, doesn't it?
I don't see why they can't cosplay him with other various things. Like his cellphone, or the extremely long handcuffs? Cake would just be a hazard to hold...