Sure you can, because anyone with a basic understanding of the English language can understand the first half is basically editorial.
If it said, “The national umbrella parade being necessary to the morale of the free state, the right of the people to keep and bear umbrellas shall not be infringed”, would you argue only those participating in the parade had the right to umbrellas?
From a purely actionable point of view, the 2nd Amendment may as well say, “blah blah blah blah blah, the right of the people to keep and bear arms shall not be infringed”. I mean seriously, if the 2nd Amendment in its entirety were on a 3rd grade English test followed by the question, “to whom does the right to keep and bear arms belong?”, the only correct answer would be, “the people”.
The militia “could” possibly be called the why, but it is absolutely NOT the who.