The traditional US measure for limitations on individual rights is when they present an immediate danger to others.

This is not shared in all jurisdictions. You're making a US-centric argument about a not specifically US issue.

I should be able to procure and own whatever implements I see fit for securing that right, as long as it presents no immediate danger to anyone else.

This is the point of the argument about escalation. In a jurisdiction like the UK, where you have no reasonable reason to assume that an attacker will be armed with a firearm, largely because of restrictive gun laws, relaxing those laws for self-defensive purposes would mean that gun ownership rates (by both law abiding citizens and criminals) would increase rapidly. In a jurisdiction with a history of low gun ownership due to legal restrictions, relaxing those restrictions would definitely present a danger to other people, by allowing criminals to arm themselves.

In a jurisdiction like the US, by contrast, where gun ownership rates are already very high, imposing restrictions on legal ownership of firearms would have a long enough lag-time until you could expect criminal supply to dry up that you could argue that such measures were putting law abiding citizens at risk by reducing their ability to defend themselves against criminals armed with firearms.

A more compelling argument can be made against carrying firearms in public or storing firearms in an unsafe manner,

In a jurisdiction like the US, I think this is a very valid argument. I personally believe that even in relatively gun-saturated environments like the US, it should be illegal to publicly carry a firearm - there should obviously be exemptions for people with hunting licenses who are in the process of hunting, or going to/from a hunt, and transporting a non-hunting firearm between legal-carry areas (to clarify, I think that legal-carry areas for a handgun or other non-hunting firearm should be limited to shooting ranges and your own home and vehicle).

owning a firearm itself is not inherently dangerous to anyone else. In fact, there are many more commonplace objects that we have that are inherently more dangerous than firearms (stairs, pools, etc...).

An individual owning a firearm is not inherently dangerous to anyone else. However, a jurisdiction with high levels of firearm ownership is a more dangerous place to live than a jurisdiction with low or nonexistent levels of firearm ownership (homicide numbers in developed countries show a positive correlation with levels of firearm ownership).

An analogy can be made to vaccination - In a society where almost everyone is vaccinated, it is actually better for you individually to not be vaccinated (although risks are very low, and the autism thing is a myth, there is a low but real probability of harmful side effects for most commonly used vaccine). However, if everybody took this view, and nobody was vaccinated except for you, your risk of negative effects is significantly higher than if most people got vaccinated regardless of if you personally have been vaccinated. Similarly, being the only gun owner in a society with low gun ownership is great, but living in a society where everybody has guns is significantly more dangerous, regardless of if you own a gun yourself.