If that were true, wouldn't the proportion of crimes involving a firearm be consistent the world over?

Surely there are many factors that would drive that. Widespread availability of inexpensive guns being only one. Punishments for unlawful possession being another that vary wildly across the globe.

In general, I don't disagree but isn't the second point ultimately a tautology? Certainly an otherwise law abiding citizen might arm themself with no intention of committing a further crime.

True. In general, the more laws there are, the fewer law-abiding people there are, since there are more laws to violate.

For example, I don't think the recent decriminalization of weed in various US states probably hasn't caused very many people to start using it. But in the same way, the laws against it didn't do much to limit its use.