Arming police has always been seen in the UK as creating a power imbalance between state and citizens. In the US, this perception of imbalance has been avoided because citizens are armed as well - making society overall, more armed, and
debatably, more dangerous.
The support for arming police tends to follow the endless cycle of political "law and order" political campaign debates and isn't always evidence based, rather it is an emotional issue. Police in most countries where they go largely unarmed, tend to still have access to firearms - be they carried in car or available dependent on circumstances, they're just not carried when a lighter touch is necessary. Police when polled, tend to want access to firearms in response to the likelihood of terror attacks, rather than because they want them for daily duties, and even then their polling isn't overwhelming (trending 60-40 range) - significant numbers of police still prefer to go unarmed because of the benefit it has when interacting with vulnerable groups - even in the face of gun crime. Guns tend to be a crutch that is easily reached for in a situation - escalating, rather than looking to other means to de-escalate"
The influence of Peelian Principles was clearly referenced last year in New Zealand. Where after the
Christchurch mass shooting in 2019, Police trialled permanently armed units. The trial was eventually cancelled because as the New Zealand Police Commissioner stated: “[They] do not align with the style of policing that New Zealanders expect - We have listened carefully to that feedback and I have made the decision these teams will not be a part of our policing model in the future. How the public feels is important.
We police with the consent of the public, and that is a privilege.”
Speaking as someone who has lived long periods of my life in countries where police are armed, and others where they are unarmed, there is an noticeable difference in the trust with which police are treated by communities. It is noticeable even between culturally similar countries with similar crime rates such as Australia and New Zealand where there is even a lot of interaction and training shared between police forces across borders.
It's a fascinating debate that might be better served by another thread. Although 'tough on crime' does tend to be a hallmark of conservative political campaigning/fear mongering, so I guess it is relevant. I also understand how it might be hard for those in countries where police are routinely armed to understand how not arming them might actually improve how they interact in society. But ultimately I think it is captured by the statement policing
for society, not policing
of society.