There are some things that I think would need to be done with or before this.
One thing to remember, unlike AZ, is in TN it is illegal to carry a firearm, it is not a right. It is a privellage that 3-4% of the population have bought from the state. So the state has basically just allowed property owners to choose to not allow the privellage to extend to their property. So until carry is truly a right in TN, I'm not sure you will ever be able to remove the weight of law from a posted sign.
Also...if you are going to hold property owners liable for posting their property, then those that doen't should be immune from civial liabilty for the actions of those who do carry into their place. I know some places post simply because the owner is anti-2A, but I'm sure some also post in an effort to try and reduce their liabilty in case of a shooting in their place. Because let's face it, most of us on here (or me for sure at least) don't have deep pockets, so if you shoot someone in McDonalds...or even worse, hit an innoncent while shooting at the BG....you know McDonalds is going to be named in the suit because they have the money....if they pay to just make it go away. Trouble is...IMO McDonalds didn't do anything wrong allowing you to carry in there, they didn't make you pull the trigger and shoot (BG or innoncent) whoever you shot, so why should they have any liablitly?
In TN property owners already have a duty to protect you from a threat they know about or should have known about, just not from a general threat (the threat of simply being out in public)
I'm not saying I'm against such a bill/law, just that there are other things to consider along with it....