>Which is still important, but not a serious military use.
A side arm is most definitely a serious military use. If we take a block of charging knights for example, only the front rank is going to get any real use out of their lances, for those behind that sidearm is where it's at. A pikeman with a foe past his point, an archer finding himself in melee, both will have their sidearm serve well if they are to survive.
And as the sword remained immensely popular in 15th and 16th century Europe, it doesn't seem like a weapon only fit for poorly armoured times.
Now any weapon is situational. But if anything it seems that the sword may be your best overall bet. Ritsu Otake for example, head instructor of Katori Shinto Ryu, holds that while the sword isn't always the best, it is the weapon which will give you the best chance in the greatest number of circumstances, against the most different weapons (see Amdur, "Old School"). And in between that and Europe:
"[The sword] is (such) a good brother that it does not become inactive in wide or even narrow places. One needs it on the sea and on the land and in crowd. On a very windy day the lance becomes a burden for its possessor, but this (the sword) never becomes useless. And on that day the archer can not shoot his arrow straight, (therefor) no one can do without the sword."
"Although they have many weapons, they would never be able to do without the sword, but those who have swords can do without all the other weapons."
Kitab al-Furusiyya va'l-Baytara, 14th century
The sword also appears in, well, basically every culture that can make them, often as one of the main wepaons. This suggests that its useful in a wide range of situations.
And contrary to most "primary" weapons, the sword is (usually) somethign you can simply have hanging from your belt. Dragging around a halberd as you go about your daily life, or fight with another weapon, would be hard.