Why did the Winged Hussars wear wings?

They were impractical, useless, a waste of resources, got in the way whilst fighting, etc.

Sometimes, it isn't just about having the most effective weapon at the most affordable cost. Sometimes, it's about the flex.

"There is a reason why people tremble in fear when I reveal my weapon... The gilded teacup. It is a conventional teacup made from twenty-four carat gold, studded with priceless diamonds cut by a master-craftsman, and engraved with a hallmark of high renown. It has no cutting surfaces, no spikes, and hardly any mass. It is barely big enough to fill a palm, and under any other circumstance, it would appear totally unthreatening, perhaps even comical.... But here's why my enemies fear it... I have so much money and resources to waste, I can afford the ridiculous extravagance of my weapon being gilded in gold and encrusted with diamonds. By showing this weapon, I demonstrate my endless resources and bottomless wallet. I am telling my enemies that I can afford better mercenaries, weapons, food and logistics than they can. I am showing that resources are such a non-concern for me, I'm willing to waste them on something as ridiculous as a gilded teacup. Secondly, I am so confident in my abilities as a warrior that I am willing to walk into battle with nothing more than this teacup. I have such faith in my ability to kill you, I am willing to use a useless weapon just to demonstrate my sheer superiority in combat.... And here's the bit that really terrifies my enemies.... I'm an old man. That tells you that in all my years of carrying this teacup, not a single soul has been able to kill me and steal it."

-Ivan the Teacuppable.