not sure of who the guy with the Wisconsin Badger logo is but no not all public lands in Wisconsin require you to take your stand down at the end of each day.
you should read your regs as you stated. in the Chequamegon and Nicolet nat'l forests, you can leave them up from beginning to the end of the season. These are Federal lands, yet public.
Now getting back to the subject, there are hundreds of thousands of acres of public shooting land in most states. what we as hunters do is we all seem to flock to certain sections of it. If you drive down the road on opening morning, you will see certain parking lots and sections of road littered with vehicles. then a mile down the road there isnt a soul in sight. go around the block and nobody is on the other side.
you'll notice that most of these heavy hunted areas have walking trails well groomed and large open areas where the hunters can see a ways.
if you look a little i bet you can find several hundred acres that are barely hunted by anyone. I have hunted public land for over 25 years and have harvested more than one deer each year.
good luck to all.