Generally, we think that Memphis is the sort of place where there are just enough options for getting around the city without a hire car, that you can probably manage it. Although there is ample car parking at Graceland, you can also get there it from the downtown area in about 20 to 30 minutes, depending on traffic. Historic downtown Memphis is certainly walkable, and although fixed rail services are pretty limited, buses are adequate.
The more scenic parts of Tennessee tend to be further to the east. Given the air service in Memphis has been so heavily downgraded, you’re unlikely to fly here to then carry on, for example to the great Smoky Mountains National Park. It’s much better to head to Knoxville in the first place, or if you are travelling from further afield, to head to Atlanta and pick up a hire car there.
Memphis car hire verdict = no.