Experiment
I cut some trees in about a 50x50 yard opening.This was two years ago.Sunlight hits this spot now in a good part of the afternoon.Bushes,oaks,berries,maples,cherry,and other lush green growth has come in.The deer love it.Now if you go just a couple of yards into the shade there's basically nothing but ferns.Let the sun in and it will come.New growth that is.
The bottom line is you can kill the deer off completely and without sunlight nothing will grow.Open up the canopy and you'll get new growth.If you get a chance try this experiment on your land.
I have no doubt the browse issue has been over rated.