I agree with JJF that the sword teaches applied distance. Unarmed one distance, knife another, sword a third. You learn to adapt to the situation.
Also it teaches directions - primarily the need to stay completely clear of uke's attacking direction
I do some iaido, parallel to aikido, and find it rewarding in many more ways than I know to explain in words.
And in aikido there is tegatana
, the hand as a sword, which might seem odd but actually helps a great deal in learning how to improve the techniques.
And so on, and so forth...
Yes, the sword art relation is quite rewarding in aikido.