When you fight somebody, you use your body as a weapon. Why is it that we differentiate our bodies so much from the objects outside of our bodies? Armed and unarmed fighting are essentially the same thing. If you train only one at a time, you could (and probably will) fall into one of the two categories – thereby limiting yourself in real confrontations.
It’s basically the same problem as being “fair“ in a fight. No eye-gauges, no groin strikes, no biting – that’s fair, right? But if you don’t recognize the potential of these weapons and if you never train them, you limit yourself severely in a true conflict. Granted, they are pretty hard to train. I mean, who wants to get kicked in the nuts? But you can always go for it and stop at the last moment, or strike nearby to the target. You can, at least, become aware of the fact that this exists and that real fights include such stuff.
It’s the same thing with weapons. What’s stopping anybody to take a knife out during your supposedly unarmed fight? Just because you started with fists, doesn’t mean that it’ll end only with that. The same thing goes in the other direction: if you’re sword fighting or doing Escrima or whatever, what is stopping you from kicking your opponent? While his attention is occupied by the weapons in your hands, a fast side-kick is a perfect thing to do to open him up.
In practical terms, I would advise to include weapons in standard sparring sessions. Why not take out a plastic blunted knife when you have the opportunity? It’ll make you much more aware of your environment during training which will translate into a greater fighting capacity in real life. Why not grab a chair and use it to keep a distance? Why not throw sand at somebody? Why not roll a magazine and use it for hitting? The options are plentiful, yet we all train either armed or unarmed, unaware of the fact that this distinction doesn’t exist in real life.