Because it was intended for one hand use, the katate-uchi was often wielded with either another weapon or a shield. Wielding the katate-uchi with a shield allowed for a higher level of defense. With that said, however, shields weren't particularly popular or widely used in feudal Japan. Most samurai warriors preferred to carry and use two swords instead of a sword and shield.
Umm, this sounds like bs (not from you, from that website). I don't think there are any historical records of any soldiers from anywhere ever using dual weapons regularly. This was occasionally done in dueling (Renaissance Europe, or even Musashi supposedly in Japan), where the smaller off hand weapon served for defense, but on the battlefield, it would be literal suicide (a short blade is not very good at parrying arrows and polearms and the like).
My uneducated guess would be that if one-handed weapons WERE used in a setting where shields weren't common, it would probably be for horseback usage (so the other hand would be free to control the reins, plus dual wielding on top of a horse is awkward), or just as a smaller sidearm that gets less in a way.