They did mention reasonable control, but gave specific examples to make it clear what that is.
However, it does appear this does not threaten “may-issue” regulations as it would perhaps still be “reasonable” even to Scalia here (keep in mind he had to keep Kennedy to be victorious).
I will take this ruling over anything else; it still is pretty broad and a big victory for us.
In a "shall issue" state, there are specified, concrete criteria which are the only reasons for denial. In a "may issue" state, denial is subject to the arbitrary opinion of the issuing authority
The decision means that any "may issue" denial may be the subject of a lawsuit, with the issuing authority being required to show rational cause for his denial, and would lead to "may issue" necessarily having to be "shall issue"