Stircrazy, Luddites not only rejected technology they actively attacked it, dismantling and sabotaging machines and burning factories. In this case we are discussing the control of mobile phones in a primary school environment, slightly less drastic I think!
I agree mobile phones do not cause bullying and removing them doesn't stop it but what they do is provide a forum within the school to which people not party to the "conversation", say for example the adults, have NO access and can exercise control only by limiting access to that forum. Limiting the usage of phones in schools is probably never a policy in isolation but is part of a set of policies relating to norms of behaviour, each of them have arisen in response to a problem or an identified need and the use of phones is no different. It presented an opportunity for troublemakers and for messing and for distraction (and not matter how good children are, it takes a very unlikely child to not test the rules and not engage in horseplay to some degree). As I said, blocking signals is not an option so the phones cannot be reasonably disabled within the school property at the behest of the school. It is true that it is possible to sneak in a phone but it is easier to define the transgression as the evidence is far more solid that a phone was present than that a phone was on. What I am saying is that I understand what you mean, the phone isn't the issue, the behaviour is. But what I am getting at is that the transgression is better defined and easier to police and the solution is more effective if the rule is "No mobile phones are allowed in School". A rule that cannot be enforced is useless or worse.
To address your other points. The child can be bullied out of school on the phone yes but at that point it is the duty of the parent to monitor what is happening on the child's phone, same as if they are being bullied on their Bebo page or similar forum. Sorry if it seems a cop-out but it is nonetheless true.
As for the child being bullied on the way home from school and being "rescued" by being able to use their mobile phone to call someone. How quickly do you think they could call for aid and more importantly how quickly that aid will come? How quickly would the phone be taken from the child? The school ban won't stop bullying but it may help ameliorate the problem, every opportunity for bullying thwarted is one less incident.
The ban on phones is no more onerous than one on swearing, wearing too much jewellery, wearing a uniform or any one of several dictats we have all been faced with in school. We all have stories of "heavy-handed" application of the rules, and while we all moaned about them, laughed about them, rebelled against them, argued with adults over them, made representations to adults about them; I would disagree with you, they didn't make us distrustful or resentful. Today's rules won't make today's moderate and well-behaved schoolchildren distrustful or resentful either. Application of a rule is not being heavy-handed. Like I said, phones aren't a special exception, nor are rules against them.
One last thing... evidence means one thing for certain, the incident has occurred. Prevention is always better. Trite but true.