You are right about the level of scrutiny being important. But Scalia expressly refrains from setting one. He refers at one point to the fact that regulation may not be arbitrary and capricious. That's a pretty low standard in and of itself. But he did not set the standard, he said the DC gun ban did not pass any available standard. I suspect not setting a strict scrutiny standard was the price of Kennedy joining the majority opinion.
Under "strict scrutiny", almost no legislation would pass muster. Under Kennedy's, every gun-grabbing legislation would be constitutional.
So the scrutiny level is a victory we still have to win.
The other victory we have to win is to get the amendment applied to the states, the way the rest of the bill of rights has been applied as against the states. As it stands now, the 2nd amendment has nothing to do with a gun-grabbing piece of legislation passed by the CA legislature. It only applies to D.C. and to federal control of firearms. The wording of the amendment is "the rights of the people shall not be infringed" not "Congress shall make no law . . . " as in the first amendment. So the second amendment seems to me to explicitly cover action by States without resorting to the 14th amendment incorporation doctrine.
“Under Kennedy’s, every gun-grabbing legislation would be constitutional.” should be:
“Under Stevens’, every gun-grabbing legislation would be constitutional.”
Under any of the standards of scrutiny that we have applied to enumerated constitutional rights,27 banning from the home “the most preferred firearm in the nation to ‘keep’ and use for protection of one’s home and family,” 478 F. 3d, at 400, would fail constitutional muster.
By using any, that means all. That means strict scrutiny is included.
I think you mean either Bryer's or Souter's. Kennedy didn't write a concurrence. Bryer was the one who wanted the "balancing" by judges on a case by case basis.