There is another reason I think it's possible, though.

[ He just adds after she's finished, but he's not smiling as much as in this icon... Ignore that. ]

We never found a murder weapon that fits nicely. If it's the chain, the imprints are a problem, it it's a bat, then that certainly couldn't be used to cut off someone's head. However, your spears don't need to be hidden or cleaned. They have the blade that could be used to make the cuts, the polearm that could be used for the beatings, and they do not linger long enough to be evidence for us to use.