There is melee fencing. Which isn't back and forth. But the electronic scoring system doesn't let you walk around a whole bunch, which limits tournament play to speedball fields... Uh... I mean fencing strips.
Interestingly enough, epee isn't a widely used sword in fencing. Just like rapier kits or any of a dozen other swords that are rare to see in the sport. I did saber and learned foil, because it complimented saber on the strip. "Real" swordplay is apparently in the eyes of the beholder. When light swords were popular, they were more lethal than heavy swords and all men of any importance carried them.
My dad and his dad also fenced. My dad had an olympic spot in the 70s but didn't go for some reason that eludes me at the moment.
YouTube - Rapier Boat Battle
^SCA fencing.