Suppose that the public land is sandwiched between two private owners. Which of those private owners must grant the access?
Worse, suppose that that chunk in the middle wasn't originally public land, but is later purchased by the state. At that point, the previous owners - having done nothing on their own - are suddenly encumbered with a right-of-way across their land, decreasing their value. This sounds like a taking to me, and thus subject to the 5th Amendment. (IANAL)