I think practically speaking, if you have a daughter, you are best off speaking to your daughter about this in an age appropriate way rather than writing to the school. [Edit - or even if you have a son, all of this still applies obvs.]
If the head thinks Be Kind is the way forward, she will not understand criticism of it ("who wouldn't want their child to be kind?! Does she want her child to be a bully?!")
Instead I would drip feed your daughter with little role plays and conversations and instil in her the confidence to say no, politely, to things that are kind-but-unfair.
I've done this with my 4yo dd a lot. For example the pudding example above, I don't praise my dd if she gives in to her brother trying to beg for her pudding, I say "wow why would you give him your treat, he's had his own! That's not fair!" And I tell off my ds for even asking (he's only 1 tbf). Whereas I know many parents (eg my dm) would applaud, how kind! She gave her brother her treat! Fuck that. No.
Recently in the playground an older girl came over and asked dd if she could play with her and dd said bluntly "no" and the girl was really taken aback. I told dd it's best to say "no thank you" but fair enough not to play with someone if she didn't want to. I know many parents would have said it's always best to say yes to be kind/friendly, bollocks to that, I won't make her prioritise someone's feelings over her own.
However we are strict about things like turn taking or saying rude things.
At the end of the day, you have a lot more influence over your child's values than the school does.