1) Improved coordination

Training with weapons improves your coordination in ways that only controlling something that you don’t have nerve endings in the can.

2) Weapons of opportunity

It’s not just a stick. It’s also, potentially, a sword, or a baseball bat, or a lead pipe. By training with a stick, you’re also training with anything cylindrical of roughly the same length. You’ll have to make adjustments for weight/length/feel, but you’ll be better equipped to fight with a pool cue if you’ve trained with a bokken than if you haven’t. The same principle applies, to some degree, to other weapons, though I can’t think of any readily available analogs for soft weapons like a chain whip or nunchaku.

3) Historical preservation

Whether or not this is important to you is another matter, but many people choose to practice with historical weapons, a category which many martial arts weapons fall into because they want to preserve, or in some cases, reconstruct historical weapons practices. This can be because the weapon belongs to a martial art they’ve already invested time into. It can also be because of cultural heritage.

5) “My Hand is my Sword”

That’s a karate saying, based on the idea that, since they didn’t have weapons, they would use their hands as their weapons. This reason actually relates, in a way, to reason II, in that a weapon can serve as an analog for an empty-handed technique. For example, in Kali, we structure our strikes by angles. Angle 1, for instance, is an inward-moving strike to the side of the head/neck. This can be expressed either with a stick or with the hand as an inward chop to the neck. Whether or not you do Kali/Escrima/FMA, you will learn angles by learning weapons. It can be easier to learn angles with weapons, because the angles will necessarily be larger, and therefore easier to see.

5) Defense Against Weapons

Even if you have no desire to learn weapons, because you believe you won’t use them, there still exists a possibility that someone will try to use a weapon against you. Learning how to use a weapon will give you a better understanding of the way that weapon moves, and therefore the best way to evade that weapon or disarm it.