It's down to the Local Authority. Headteachers do not have full discretion.
It's practically impossible for state schools to implement even a short, temporary exclusion these days.
My final supply stint was well over a year ago. I stopped one fight and one assault.
To be fair, the "fight" consisted of one boy who had been mercilessly provoked throwing a punch. I intervened and he accidentally connected with me instead of his tormentor.
I'd already alerted the SLT about the bullying, but nothing had been done. The fact that the lad accidentally connected with me (ironically) gave him street cred and stopped the bullying.
The assault consisted of an unknown S1 boy running into my room at the end of the period, screaming "Help me!"
He was pursued by another S1 pupil who had apparently been targeting him for some time. I managed to stop the assault and walk the assailant backwards out of the room, but was hurt in the process.
I later found out from other pupils that the victim had been attacked by the same boy previously.
In my experience, when pupils are being bullied, the victims are deprived of their education by being given permission to leave class and school early in order to give them a head start away from their assailants. It's all wrong: the mantra is that we cannot deprive the bullies of their education...but what about their victims?
This has not happened overnight - I'd say that things started to go rapidly downhill round about 2000. (I started my teaching career in '84.)
I'll add that the fact that Police Scotland often doesn't want to deal with youth crime doesn't help one iota. In my experience, it's either "We'll leave it in the hands of the school," or "Did he really understand the implications?" or - on one memorable occasion [prior to the formation of Police Scotland, to be fair] - "The statements have been lost."
I wouldn't advise any young person to become a teacher in the Central Belt. I do know some teachers who have moved to the Highlands or Islands and are much happier there.
A former colleague moved to the Highlands and was sworn at in her first week. (The only time it's ever happened to her there.) She was bemused when the HT came to her room to check that she was okay...In our previous school, the HT had told us that teachers should 'expect' to be sworn at.