Gun ownership Fee pays for Mental Health care

Although guns were involved in the Sandy Hook tragedy, mental health was the true issue, no doubt about it. Additional gun control requirements were needed, but I view it as being slightly off the mark. I have a simple suggestion on the subject of gun control.
A requirement that every gun owner register every gun they own with local police. The owner has complete responsibility and liability for each gun and its use. In addition to registering each gun, the owner pays a nominal yearly ownership fee for each gun. Not a huge sum, possibly $5.00 a gun. Every cent of that money is then provided directly to the operation of mental health treatment centers.