Not even that they get a permit.

John Doe is a multiple convicted felon, and really wants a gun so he can rob his drug dealer. He doesn't have a permit, and he can't buy one, but he really needs one. Under your plan, he could go online, look up "registered gun owners near me", and see everyone within walking distance that has a gun. If it were common knowledge that there is a publicly available registry of firearm ownership, criminals would absolutely use it to pick targets. Even criminals who don't necessarily want guns would still target gun owners, because they can sell that $400 pistol to John Doe for $1000.