True, we don't. But neither do we want the government to be in possession of a list of everyone who exercises their rights, especially when there is an alternative that addresses they reason they SAY they want the background checks.
I certainly don't think this means the government keeping a list of everyone who has a firearm.
I consider my right to keep and bear a firearm important enough to take steps to keep one of mine from falling into the wrong hands.
Sadly, it's like so much government does these days. They go after any problem with a sledge hammer, disregarding the rights of the law abiding citizen to supposedly keep the bad guy in check.