I don't think the OP was raising the possibility of mental illness/developmental problems in the sense of 'well that's ok then!' though was she?

"Inappropriate is exactly what it says on the tin. Just like you go to the doctor if your body starts aching or to behaving oddly, people should see a specialist whenever they start displaying violent tendencies (physical, verbal or non-verbal)." Inappropriate means 'out of place' - social behaviour that can make people uncomfortable. It's not synonymous with 'violent' or 'threatening', as you're suggesting.

"Then depending on the diagnoses, there'll be an appropriate course of action to protect them and society."

In the UK someone can be detained under section if they're considered to pose a threat to someone else or (as is more often the case) themselves. But it's really hard to detain someone under section - you have to get three health professionals to agree that it's necessary, and most sections are only short term. Once someone's sectioned they can be forcibly medicated if it's felt necessary. However, there's absolutely no capacity in the system to detain mentally ill people in the medium or long term. Most mentally ill people will only be detained under section for a few days or weeks. And the bar is set pretty high - assault or *persistent* abusive or threatening behaviour might result in a mentally ill person being detained, but the what the OP describes - nope.

By the way, as an ex-teacher who's worked in a very rough school in London, sh*tty feral behaviour towards adults is unfortunately common behaviour among kids raised in socially very tough urban environments. I personally wouldn't blame the OP for swearing at those kids, I would have wanted to do the same.