Pike and Shot isn't really comparable to the Phalanx: if a Roman Legion had guns and cannons, the merit of sword and shield against pike would probably be the least of a Phalanx's problems, as it's forced to either attack an entrenched enemy, or retreat.

Even in Pike and Shot warfare though, sword and shield were still being used to great effect by the Rodeleros, who were used in conjunction with pikes and guns, but were also eventually dropped for the same reason that halbreds and pikes mostly were as well: by the start of the 17th century, increases in gunpowder quality and quantity had decisively made powder the weapon of choice. As such, fending off pike squares in melee didn't require special consideration, given the losses that the pikes would take trying to advance in a formation without fire superiority backing them.

Practically all Musketeers had swords as backup weapons though, and the Highland Charge famously made good use of them, so even sword infantry didn't totally die out until bayonets became common.