Here's another picture of a Kalaripayattu training place with curved katars
It seems more common than straight ones. Granted this is kalaripyattu, a martial art from Kerala. Perhaps the people of northern and central India used straight katars more? I say this because in all the searching I have done on Shastar Vidiya and Gatka have come up with mainly straight dagger-like katars.
Check the videos near the bottom of page
It appears to be used by Nidar Singh Nihang (along with another dagger) as a "main-gauche" of sorts. It seems like a good close-quarters and bridging weapon in combination with a sword. On the battlefield it was probably secondary to longer ranged weapons like spears, bows, swords, and matchlocks.
I imagine in the old days, in city streets and alleys, a katar alone would be a formidable close-in fighting weapon in a martial world with a plethora of knives, daggers, claws, fighting bracelets, etc.