@ morph bark:
having a weapon in hand isn't as limiting in your ability to use non-weapon strikes as you seem to think. Kicks are largely unaffected for one thing. For another, you can still get a hand free even if your weapon is two-handed and there's no good reason you can't punch someone with the hand you're holding a one-handed weapon in if the enemy is too close to use the weapon effectively. You're not doing yourself any favors if you don't learn to integrate unarmed strikes into a weapon style.
The biggest hiccup in this is that the schools that teach weapon styles aren't exactly great about teaching how to integrate complex systems of unarmed strikes into their use. You really only see it in styles that start off as unarmed styles and later integrate weapon use.
BTW, the most useful weapon styles for practical application are the various stick-fighting styles. You don't have to carry a stick around, you can find something similar in most settings.