Whatever you do, the land has to be managed. "Managed" can mean a dozen things to a dozen people. Some folks want it completely untouched. Some folks want to manage it as perhaps a farmer or rancher would. Some folks want a place to ride ATVs and raise hell.
Political systems exist for political reasons. That is the only reason they exist. Lately, any political system in the States is going to gravitate towards one group throwing mud at another group.
So, to address your first sentence, I do not believe there is any way for this not to be political. Perhaps the key question instead is this: at what level of politics should these decisions take place? Should everything happen at the national level? If so, why? Personally, I'd prefer a limit of thirds between national, state, and local governments. That way any one political group doesn't start monopolizing all the power. It shouldn't be possible for us to have a single election at any level of government and decide how to treat huge sections of public land. For that reason alone, I'm against the current trend of federalizing everything.
It's not because I want the land to be commercialized. In fact, I want just the opposite. But those are my tastes. I understand others have their own views. Let's stay as far away as possible from more winner-take-all political structures.