Disclaimer: I have a personal rule against responding to the same argument more than three times so I may read what you reply but won't be responding

The total number of blocked firearms sales in the US taken in isolation is irrelevant.

I didn't take it in isolation. You said that any idiot in the US can own a gun, and I gave statistical proof that that statement is false.

Yet the total and proportional number of shootings and mass shootings is so completely different.

Congratulations, you're seeing what lack of mental healthcare access and social safety nets has on a population. Let's look at the proportional number of people who are given access to adequate mental specialists and don't grind themselves to death at work and relax by watching quote-unquote News designed specifically to induce anxiety and paranoia.

Even within the context of America:America, your argument doesn't hold up. If "More guns = More deaths," then the opposite should be true: "more firearm deaths means higher ownership," but that isn't the case. Gun ownership in the US has stayed pretty steady for the past fifty years (please see the legend), yet gun death rates have more than doubled in that time. I don't see how you can look at this data and conclude that guns are the cause of these deaths (the majority being suicide), and not a symptom of something larger.

those in lawful possession would need to give up their firearms.

This is a complete pipe dream and is the reason why arguing with Europeans about US gun regulation is a waste. Firearm legislation, with a few very broad and defining pieces of regulation, is handled by states or local municipalities exclusively. The federal government legally could not enforce these laws on the state level. So, assuming that you could accomplish the Herculean task of getting all of these governments to agree, and after all appeals had gone through the courts, the seizure process alone would take decades. It's a conclusion that isn't founded in reality. You might as well be saying that we should invent a superhuman serum to prevent gun deaths.

Just so that my argument isn't being misunderstood, I want to state it very clearly: I am not saying that - in a vacuum, conceptually - full gun prohibition does not prevent gun deaths. I'm not stupid enough to say that a room of 100 people is just as likely to have such an incident if one of those people has a gun as if none of them do. But I believe that that same room of 100 people is more likely to have an incident if one person with severe untreated mental illness has a gun than if there are fifty well-adjusted weekend skeet shooters with shotguns. In other words, the quantity of guns alone does not indicate the likelihood of any gun violence.

I'm saying that your argument and the conclusion thereof is horribly Eurocentric and shows a lack of knowledge on US culture or government.