I agree strongly with presenting it as a matter of etiquette and inclusion, and coming down heavily against using language as a means of bullying. Absolutely right. And insisting on a classroom language could help with that.
But I would be very concerned about a situation where a child with limited English was very upset or developed a serious problem and was unable to explain to a friend or ask a friend to translate, because their first language was banned and they were too stressed to do it in English- or simply did not have the words. A medical problem for instance- or being bullied.
Schools also have a safeguarding role: how do you manage that if a child who is being abused at home cannot communicate with the teacher because her own language is not good enough and she is not allowed to tell a friend? Some of the foreign speakers in this country have come in as refugees; they may well be traumatised; how can they open up if they do not have the language? If we use interpreters for adults, how can we ban children from using a friend to interpret?
My own ds went through a period of selective mutism which was clearly related to bilingualism; not a massive problem in his case, but then he was a healthy non-traumatised child from a privileged language background with a relatively prestigious second language and a well functioning family with excellent double language skills who were able to help him out of it, so the fact that he didn't speak at nursery or for the first year or so of primary wasn't a massive problem: there were people there who could speak for him.
If rules are introduced re language use, I think they should be very carefully thought through and carefully worded, so that the children understand that this is not about your other language being less appreciated or wrong, it is about making the lessons work and not making other children feel excluded. And a special explanation about emergencies.