it may be that the court will say that it is up to local governments to set their own restrictions, but the federal government is prohibited from doing so...
much like the eminent domain issue...
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I don't think that the ruling will be so sweeping. Such a ruling would automatically decide the 14th Amendment incorporation issue, which isn't before the Court. They will address (IMHO) only restrictions on the Fed.gov, as DC's government is a wholly-owned subsidiary (i.e. it literally exists because of a Congressional resolution and, therefore, is subject to the same restrictions on its actions).
I don't know the result (though I know what it SHOULD be), but one thing I know for certain - there will be more gun cases in federal court, and soon. If the SC substantially or wholly upholds the Circuit Court decision, then a case will be filed against Chicago using this case as a basis for the claim, and reasoning that the 14th must apply the restrictions on the fed.gov to any state or subsidiary thereof. My understanding is that the case is ready to be filed, with just a bit of detail work and polishing necessary.
That would not work in DC. The Congress has Plenary power over DC. IF anyplace is considered part of FedGov territory it where the US Constitution must prevail it IS DC!