[Ruy Dias de Bivar]

You could not do that if the carrier had spears and swords.

Maybe the attackers could throw armour piercing pilums at the carriers.

http://romanmilitary.net/tools/pilum

[philman_36]

You could not do that if the carrier had spears and swords.
True, but they don't in that picture.
I wouldn't even consider such a tactic if they had those weapons. Better then to go with fire as circlecity suggested.