After a cursory glance through the DMG...

... it looks like all swords and most weapons, outside of generic +1, +2, +3, or "Vicious" weapons, require attunement. Rods, Staves, Oathbow, Vorpahl Sword, they all require attunement. It seems that anything that can be wielded as an offensive weapon that is held in the hand(s), even something like Ring of the Ram - despite there being several rings to which one doesn't have to attune - require attunement to benefit from the magical properties therein.

Not having the Sword of Sharpness require attunement would make it the lone exception.

After a cursory glance through the DMG...

... it looks like all swords and most weapons, outside of generic +1, +2, +3, or "Vicious" weapons, require attunement. Rods, Staves, Oathbow, Vorpal Sword, they all require attunement. It seems that anything that can be wielded as an offensive weapon that is held in the hand(s), even something like Ring of the Ram - despite there being several rings to which one doesn't have to attune - require attunement to benefit from the magical properties therein.

Not having the Sword of Sharpness require attunement would make it the lone exception.