That is not a bug, but a feature.So my grandfather leaves me several firearms when he passed away. How is the city going to find that I own them? How is the city going to find firearms that people brought with them if they recently moved to San Jose? This doesn't sound like some put much thought into this concept. I really don't see much traction on this new law.
The first thing the city will do is force you to report all of the firearms that you own. Its a tax, see. And the SCOTUS has already said the government can tax you. They can also force you to purchase insurance - see Obamacare. Its a tax.