Most families (who likely pay the most in property tax) live in the surrounding suburbs, which as you have noted are indeed much higher in terms of property tax. Similar suburbs around Nashville are averaging 50-70% lower property tax rates, which is significant enough to move oneself out of the state. This is only going to increase the tax burden for the remainder of residents of the state. The city proper only comprises 2.7m residents per the 2010 census, while the metro area is 9.5m residents.

My evidence on the other items is anecdotal, but that is my opinion and I'm understanding of the fact others may disagree.