Some children hit their parents for fun
Surely hitting them back just tells them it's OK to hit people so long as you're bigger than them?
naughty child tries to run away from parents. Parent grabs child's arm as potential risk to child going missing. Parent has now commited an assault and at risk of prosecution
Not an issue. All that would happen would be that the current defence of reasonable chastisement would be removed; other defences such as the use of reasonable force in self defence or to prevent harm would remain in place. They work OK for assaults on adults and non-related children, there is no reason why they shouldn't for assaults on the accused's own children.
I don't think it would help anyone, including children, to prosecute parents for something very minor.
I doubt that they would be prosecuted for minor offences. However, the fact that they have, for instance, had a formal warning or caution from the police may well be all that is needed to keep the child safe.