You miss the point. The land is privately held. It is not held by gov.org of any stripe. You seem to prefer the non-discriminatory nature of public lands and the right to shoot wherever you damn well please. It ain't that way here. Now, go on and shoot in your public land Utopia and deal with the attendant problems associated with it.
By the way, there are places to shoot MGs around Austin. I've done it there, Kerrville, Camp Wood, Leona, and several other places around the state. You see, the problem, if you want to call it that, is those places are owned by private parties who are not keen on opening their land up to just any Tom, Dick, or Harry that comes down the pike wanting to blast away. It's not always about "I have money and land so fuck you." They have the right to discriminate a little as to who comes on their land. Some might even deny the PRIVELEGE of shooting on their land just because they might think a prospective shooter is a dick. Now, I don't know that the OP is a dick and I'm gonna assume he isn't, but, I support that right of the property owner. I support private land ownership. Maybe some day you'll get rich and want to come back to TX and buy you some land to shoot on. Or, maybe not.