You missed the big one as far as cons...
The National Instant Criminal Background Check System is a federal system.
It should only be used when interstate commerce takes place.
If you search out and read the texts of all the bills put before congress that deal with this, you'll see how carefully they dance around the interstate commerce clause.
Because the congress people know that's the hardest obstacle they have to overcome.
Please don't be fooled into just handing this to them on a silver platter.