States with the most resident participants.
Texas
Pennsylvania
Michigan
Wisconsin
Missouri
Being from a State on this list, I can generally believe that access is a key (also culture, youth participation, and CERTAINLY, too many people). Here, in Wisconsin, about 1/6 of the land is in public ownership and something more than a third more than that in private ownership with public access. While this is not evenly distributed across the state, there is lot's of public access for hunting.
In addition to public lands, much commercial/industrial forest land in the Northern part of the State receives favorable tax treatment but must permit access for hunting and fishing although vehicles can be prohibited (thankfully).
In the southern areas where pheasants dominate, private farms land is nominally leased for hunting access with some restrictions related to harvest times. All my pheasant hunting is done on such properties which tend to have less pressure than true 'public hunting grounds". Other states have similar "walk in' programs adminstered by the state.
Hunting access is not as free and easy as it was when I was a kid in the North and you just walked outside and went hunting almost anywhere, but the opportunities are still plentiful.
Public perception has certainly changed! When I was going to college here in Wisconsin, we would climb on a City bus with a shotgun, take the bus to the outskirts and then hitch-hike to a hunting ares. I hate to think of what would happen if anyone tried that NOW.