The late Justice Burger held a private (unofficial) opinion in opposition to the majority of constitutional scholars. To his credit, he never let that private opinion impinge upon his professional capacity. As a private opinion, it is marred by both historical lacunae (I hope 133 independent states is a typo!) and personal whim.
First: States did form militias in Colonial America. --So did municipalities and townships. Burger failed to even mention that fact, let alone deal with its implications and his reasons become apparent farther into his treatise.
Second: The National Guard is an extension of the standing army ultimately under federal control. It is not analogous to either state or local militias in the colonies.
Third: Burger puts the cart before the horse by asserting that the right was predicated upon the militia. The historical fact is that militias were formed (and dissolved) as needed and were therefore far more avocational than vocational. In contrast, the right, spanned multiple militia iterations facilitating their formation. In other words, it did not "turn on" and "turn off" with their formation and dissolution.
The ludicrous nature of Burger's argument becomes apparent if we attempt to impose his view upon some other need when stated in the same grammatical framework: (i.e. A prefatory and operable clause respectively)
A well regulated public reading program being necessary to the literacy of a free state, the right of the people to keep and own books shall not be infringed.
In this hypothetical scenario, a need is stated and a right is guaranteed to facilitate that need. The sentence structure is slightly archaic today, but not out of place in period literature. No one would suggest that the right to keep and own books is predicated upon participation in said reading program and therefore limited to the auspices of a public library or similar institution. The right is clearly a prerequisite of the need. Similarly, arms were needed to form a militia. Guaranteeing an individual right to own them made it possible to form a militia when it was needed.
Fourth: Burger's observation that standing armies have become a necessity is an argument of obsolescence vis a vis the Second Amendment. Let's assume for the sake of cordial discussion that the Second Amendment has become anachronistic. There is a prescribed method for changing and amending the constitution and it is not judicial review launched off the springboard of historical revisionism. (Again, Burger to his credit, seemed to realize this in his professional life.)
Fifth: Burger attempts to compare the capabilities of firearms today with those known two centuries ago. While it is true that a weapon of two centuries ago suitable for confrontational purposes has very roughly the capabilities of a sporting piece today, this is irrelevant because the simple fact is we never interpret the constitution like that. Just as the First Amendment protects modern forms of communicatoins and the Fourth Amendment protects modern privacy concerns, the Second Amendment extends prima facie to all instruments that constitute "Bearable arms."
Sixth: Burger goes off the reservation entirely by asserting that hunting, fishing and owning automobiles are "Rights." Even if we ignore this piece of fiction, he has it exactly backward again. The Second Amendment is about arms serviceable for confrontational purposes, not recreational use.
Seventh: (And this is directed more towards the original assertion than at Burger) Burger did acknowledge the right to self protection (Ostensibly with a firearm) He explicitly said that the right to protect "homes" need not be challenged. He proposed registration of firearms, not the curtailing of an individual right. Burger at no time ever explicitly stated that the "People" of the Second Amendment were different than the "People" of the First, Fourth, Ninth and Tenth amendments.