To answer the question posed - yes, they should all be armed.
I am in Norn Iron and they are all armed here. I do not travel much but I cannot remember being in another country except mainland UK where Police are not armed.
A scenario (fictional) to consider, a police officer attends at a small village in the Highlands where nothing ever happens but there has been an accident. The police officer investigates the accident and belives that one of the drivers is drunk and proceeds to process them. The driver pulls a shotgun from his car and shoots the police officer.
I am not saying that a firearm would save the officer but it might; it might also dissuade the driver from lifting the shot gun. Currently the officer, if they were lucky, could run and take cover and request assistance from an armed unit - in the meantime, they are under serious threat of bodily harm.
Without having first hand knowledge of the Raoul Moat case I cannot definitively say whether armed officers would have stopped him but the option was not there.
Consider goes to your place of employment daily, with the worry of someone causing you serious harm - perhaps even death and you have to rely on your training, your ability to talk, a baton, spray (CS or PAVA) - these will work in the majority of cases, but on the one occasion that you need something more suitable - a firearm you do not have access to it. That one occasion is the one where you will suffer most.
This is a ongoing discussion and probably will continue, risk assessments may indicate the need for all officers being armed in future and that is probably when it will change. God help any officers who are injured or worse because of the lack of appropriate means to stop a threat because of managerial reluctance to firearms and the public perception that they must only be carried by very specialist units does not help it.
A final point - are all military personnel in the SAS or similar - answer NO. All front line military personnel are armed, why does the same not apply to police? I do not see a need for very specialist training to fire a gun in everyday circumstances. ARV's still have their specific role when required.
My 2p
Hope you all have a great weekend,
Richard