So I had to look this up because Wisconsin has similar weird demographics skewing heavily toward independent. In the case of Wisconsin, its because party registration stopped some time after 2004, when I first registered (meaning I’m permanently registered as a dem, even if I don’t want to be, because we no longer have a mechanism to change it), and we now have open primaries instead.
TN is similar in that they don't require party registration, and they have open primaties which makes registering pointless. I wasn’t really able to find info on whether or not you still CAN register with a party if you really want to, but I’m kinda guessing no for the same reason you can’t in Wisconsin. They just don’t maintain those systems anymore because they don’t need them.
I don't think states with closed primaries or required party registration have nearly the same level of independent population, and thus influence from independents, but I’m sure that’s on the rise too, as dems have spent decades alienating their base.