Sure. The problem is that swords don't have much effect on an armoured opponent. There are three types of attacks you can do with a sword: slashing, stabbing and cutting. Against a gambeson (jacked made of 20+ layes of linen stitched together) stabbing works, slashing is hard and cutting mostly doesn't work. Now add a layer of maille over the gambeson. Cutting doesn't work at all anymore, slashing probably only bruises you or breaks some bones and stabbing only works with narrow and sharp-tipped swords. Replace the maille with steel plates and you're pretty much invulnerable to swords, except at the joints, eyeslits, etc).

So, sending out a group armed with swords on the battlefield isn't going to do much. You want warhammers with backspikes that can pierce steel plate and crush bone, halberds that can hit so hard it crushes anything underneath armour, long pikes to keep the enemy at a distance, bows to pierce maille. The best weapon on the battlefield is actually mass. Get a group large enough close together and trample your opponents.

That's how most battles were won. In viking and early medieval times you would use large shields and short spears, create a shield wall and run over your opponent. Later on heavy cavalry appeared who could easily run over them. Cavalry dominated until the English started using the longbow en masse to kill the mounts of the cavalry. Swiss pikemen started using 6+ meter long pikes in tight bock formations. These pikes were so long that cavalry could be stopped dead before they reached the pikemen in a charge. It's like a wooden cumple zone. That pretty much spelled the end of heavy cavalry. Then soldiers started using halberds to get in between the pikes and crush pike blocks.

Swords were often carried on the battlefield but usually as a backup weapon, not as the primary weapon. Their cross shape granted them a lot of symbolic meaning in those religious times, but there are much better weapons available if you want to win large battles.