To assume such is to read additionally restrictive language that is not present into the right. I see where you're coming from but I think it's the starting point of the anti-gun slippery slope to start looking to unclear contextual combinations or alternative meanings. The words are there and make perfect sense on their face. It's followed by "shall not be infringed," about the most aggressive rejection of government regulation to be found. The First Amendment says "Congress shall make no law". That is focused on the legislative branch and leaves wiggle room for executive orders and judicial interpretation. "Shall not be infringed" is a far stronger condemnation of governmental meddling. I would have to say that is strong support for a broad interpretation for the 2A, which is why I subscribe to the clear, simple and broad definition I've put forth.
There's certainly plenty of good argument beyond that but I'm trying to keep it point blank to avoid spinning off into all sorts of tangential mental exercises and longwinded justifications.