Should we think of 5e’s greatsword as an especially beefy longsword, still able to be carried at the hip?

Historically, greatswords were so long they were impossible to carry at your hip, so you typically carried one around with it resting, point-up, against your shoulder. One benefit justifying this inconvenience was their reach. However, in 5e, greatswords are not “reach” weapons. Should we therefore think of the 5e greatsword as just an especially beefy longword–twice as heavy, but still short enough to be carried at the hip? Or, since we’re telling fantastical stories about fictional epic heroes, do we simply buy into the Hollywood back sheath, no matter how unreasonable that’s been shown to be in real life?

Bonus Question: Does your same answer apply to 5e’s other heavy and 2-handed but non-reach melee weapons, the maul and battleaxe?