If it were considered a solemn, noble, patriotic activity to keep guns and ammunition, where you had biennial training and evaluation with experts, certificates, people thank you for helping safeguard the security of our communities, and so on, you could increase rates of gun ownership and nonetheless decrease the rates of gun possession by people who shouldn't have guns.
Not every country with drastically lower shooting deaths than the U.S. also has drastically lower gun ownership. It's an effective way, but it's not the only way.
One of the biggest problems with the issue is that in the U.S., enough people like guns more than they like the government that the simple "less guns" thing doesn't work. You don't get out of the pattern of doing the same thing over and over and over by trying the same solution over and over and over. At least, not very quickly.
If there's a solution to be had any time soon, it's almost certain to be found along a different path. If step one is Democrats clobbering Republicans over the head rhetorically, or any similar approach, it's a pretty good bet that it's going to be the same story all over again.