Scalia said more than that. Not only type, but how and when. Scalia made the point that the right to bear arms could be restricted. So government can make it illegal for the guy to carry an M60 machine gun on a playground even if their isn't a sign. Do you understand, yet?
What Scalia said that restrictions on the right to bear arms can constitutionally be implemented. It can not be any clearer than that.
The redneck M60 playground example is a straw man argument.
An M60 is an infantry light support weapon. As such, it
might be covered under the 2A,
ideally.
In the libertarian ideal of a 2A legal structure, it
might be legal for the man to carry the M60 onto a playground... but he may very well have cops or armed and concerned citizens approach him and ask him "WTF are you doing bringing an M60 onto a playground?" and if he doesn't have a very reasonable answer he might be questioned further... or some armed citizen might "escort" him elsewhere.
See, there is no context to this straw man example. WHY did he bring the M60 onto the playground? To kill children? Well, murder is illegal, isn't it?
Is there a loaded belt hanging out of the breech? If so, he would definitely draw the intrest of cops or armed citizens. Does he point the thing at anyone? That's assault with a deadly weapon, or possibly criminal negligence. In an armed society, it would also be a good way to get killed before you could unlimber that long heavy machinegun.
At 3', a handgun is a more effective weapon than an M60... because the M60 is too heavy and ungainly for close combat. In an armed society, people wouldn't be trembling in fear and scattering like sheep because this guy is walking around with an M60. It doesn't make him bullet proof...what it will make him is highly conspicuous.
The original intent of the 2A was to cover
all small arms and weapons suitable for militia use and other lawful purposes (sport, hunting, self-defense). Handguns, shotguns and all rifles (including selective-fire AK's, AR's, M4's) are properly covered under that definition. M60's, maybe. A .50 machinegun is a MOUNTED weapon and may arguably be beyond the defintion of small arms and light weapons appropriate to militia service; a Stinger or RPG might or might not fit the definition... it could be debated.
Explosives are typically indiscriminate killers, and carry with them a substantial risk of accidental mass-destruction if mishandled or improperly stored... so some kind of license certifying that you are properly trained to handle same would not be too restrictive IMO. This might also apply to grenades, RPG's and Stingers, depending on exactly how you define militia small arms and light weapons.
Context is always important. What kind of gun a man is carrying and where are not as important as what his intentions are. I would assure you that a man carrying an M60 onto a playground would attract notice even if it were legal, and some concerned (and armed) citizen is likely to ask him for an explanation at the very least.