We went through this with dd for about 2 years, yes, that long
We also knew which child was reinfecting the whole class. Dd used to tell us all the time that this poor kid scratches non-stop, she actually puts her cardi over her head, and rubs like crazy. Used to be so at the parents, I know the dad is a uni lecturer, and him and wife always so well turned out, yet their poor kid crawling with lice.
Everytime we got dd's head cleared up, it was becase she was no longer sitting beside / behind this child. And the cruel thing was (and still is), that none of the other girls want to play with this child, which is awful.
The teacher even had a talk with the class when said child was sent out on an errand, that the other kids (boys esp), had to stop calling her names, cos of her lice.
And, yes, I must admit, I did phone the school last term, because dd had been lice free for about 6 months, and got them again the very day she sat beside this kid again (teacher rotates who's sitting where every few weeks) Anyhow, teacher was very sympathetic, and said they all knew full well that this kid wasn't getting treated for her lice, but like OP said, nothing they can do about it, other than send out general letters. Tbh, I'd had enough, and insisted dd got moved, which I know sounds awful, but I jsut couldn't face any more lice.
One thing that really worked for us was conditioner and a lice comb (metal ones are best) Just buy a huge big bottle of cheapest conditioner you can find (supermarkets own is good) You don't have to even wet the hair first, just slather on tons of the stuff, and get combing. Apparently the conditioner temporarily suffocates the lice, so you can comb them out. Also, it reduces the grip of the eggs, making them easier to remove. You have to do this every night though, even after you think they're all gone. Other thing we did was to tie her hair up in really tight plaits every morning before school, and spray tons of tea tree and neem oil spray on (I think this is a leave-in conditioner), It stinks to high heaven, but apparently repels the lice.
So, no YANBU at all. I'm scratching here jsut thinking about them again!