You're correct in touching on the constitution
I wonder how some of the current laws have passed constitutional scrutiny (generally speaking, that is). Nonetheless, I think any federal gun law is treading on dangerous territory, in that it arguably violates the second amendment.
Arguably being the key component of my comment, with respective arguments taken to extremes on either side - and again, to say "extremes" is even subjective.
By the way, I'm not sure how to respond to you (or anyone else, for that matter) when you nitpick on words. Gee, I used the word "sweeping". Maybe I could have pulled another word out of my ash (tray) that would have been more appropriate for more people. Sometimes things just come out without having been given a lot of thought. I wish people would nitpick less and seek overall understanding more; and I think the former prevents the latter - oftentimes done intentionally, but not always.
Does registering the serial numbers of my weapons to the federal government violate the text of the 2nd amendment? How in the hell do I know? How in the hell does anybody know? Arguably, both yes and no, depending on who you ask and what their desired end result is. And it's for that kind of reason I'd prefer to start with the premise and work up (something advocates of progressivism refuse to do (because they fear to do), by the way).
Do I want to give the serial numbers of my weapons to the federal government? Hell no. That's not the intent of the federal government in regards to any of the articles or amendments of the constitution - the rules under which government must operate.