Why don't they need to know what you have? They get to know what car you drive. They even make you get a license and insure it. They get to know about a lot of your stuff, even stuff that doesn't have the capability of killing people.
I think the numbers are very relevant. If something started killing 10,000 Americans each year, I think we'd want to investigate what's going on and, if there were reasonable ways to increase safety, enact them. We did this with cars. Safety regulations, propaganda campaigns to reduce drunk driving, more safety regulations... There's a reason the morbidity is going down, and it's not just that we're getting better at emergency medicine.
Yes, the guns getting to gangs are already illegal. But it's hard to stop them from getting those guns, even though they are illegal, because there are so many ways for guns to slip through the cracks. The suggestions I made in that very post plug up some of those cracks while keeping gun acquisition quite easy for normal citizens. I mean, if you were an IL resident who buys all your guns from dealers, there would be no difference! You have to get a license to own a gun (FOID) and the gun dealer runs a background check when you buy it. Is that such a hardship? There'd be another form, maybe, but the gun dealer is already keeping paperwork on what gun he sold you, so I don't think this would really multiply. Is this tyranny? Research in illegal gun markets shows that slightly increasing the burdens puts a real hurt on that already illicit gun market.
So the reason the government needs to know what you have is that other people like you let their guns get to bad guys and we can't figure out where they came from.