You didn't read my post to the end. And some of the Staves may look weak but are, in fact, much stronger than you give them credit for - a sword that does 30 damage per hit has nothing on a Staff that does 8 DPS.
I read your whole post before this one just fine, and you simply generalized what you stated about the staves with this remark, "Staves seem to be a special case of weapon in that "magic is better". Yet, you gave no stats. I understand completely how damage works in games whether damage rates or by DPS (I've been PC gaming, especially with RPGs since 1981). When I said her sword is exponentially more powerful than the staves, they really are. She hits an enemy with her frost staff, and you watch their health diminsh 60pts/sec, when the effect wears off, they still have about 85% of their health. Lydia whips out her sword, and three swings and they are down (sometimes it is one finish move and it is over). Her sword does over 700 damage.
Now, even if she wanted to just chain the staff attack and keep adding to the effect, it still would not beat out the power of her sword.