Simply not true: https://www.google.com/#q=push+button+gun+safe (Americans are problem solvers, after all; you can also use one with a key and keep that on your person, say, on a string around your neck; this is also what hardening your entrances etc. is about, to give you time to react).
And "appropriately" is really situation specific; I haven't lived in a situation where there was danger of another abusing one of my guns for decades. There's also the pattern of keeping it in your safe until you get home (and if you're really hard core, carrying it until you go to bed). And you're completely ignoring concealed carry, which covers 42+ of the states and ~72% of the US population, 12+ million licensees, and 10 states without a license requirement: https://news.ycombinator.com/item?id=11980298
And that's before we even get into the "much more likely", which simply isn't supported by the facts, starting with a 25% drop in the number of fatal gun accidents per year in the period 1980 to now, while both the population and number of guns owned by it roughly increased by 50%.
Note that if you're depending on e.g. Kellerman's studies, they score only fatal outcomes for home intruders as successful defensive gun uses, when the majority don't involve any shots being fired, the vast majority don't involve anyone getting hit by a round, and pistol torso hits resulting in fatality only about 1/4 of the time. Even the biased CDC admits to the utility of guns: https://www.google.com/#q=%E2%80%9CSelf-defense+can+be+an+im...