Why is a matter of personal perception…
My post relates to the original question -- why these techniques? I'd like to address what constitutes a 'weapon' first, beginning with the word as defined by Merriam-webster:
Main Entry: 1weap•on
Etymology: Middle English wepen, from Old English w[AE]pen; akin to Old High German wAffan weapon, Old Norse vApn
1 : something (as a club, knife, or gun) used to injure, defeat, or destroy
2 : a means of contending against another
So, just about anything can be used as a weapon. For instance, an aluminum soda can is designed to be a 'beverage delivery system' for the erstwhile consumer, but if you tear the bottom off of an empty can it may be utilized as an improvised edged weapon. [Fanatical] Ideologies are another example of weaponry utilized in terrorism and psychological warfare, which brings us to a central point: what constitutes a weapon is an individualized mental perception, because without a brain with which to perceive, you couldn't contend with anyone. So, by definition, anything that could possibly be used as a means of contending against another is a weapon, and therefore, all martial arts are ‘weapons' based…
Why these techniques? Because there are those who believe that they embody the central principles that make Aikido a dynamic, unique, useful martial art, and a worthwhile subject for further study.
In addition, Patrick Cassidy Sensei once described the progression in Aikido, and I paraphrase here, as ‘first you learn Tai Sabaki (about your body/yourself), then Kokyu Ho (body-mind-breath coordination -- body/self), then Ki No Musubi (connecting to your partners energy -- external environment/others). So, Tai Sabaki and Kokyu Ho + Ki No Musubi = Awase (blending energy -- extending your sphere of influence).
So, learning the core waza in the beginning teaches us about ourselves, then about how we relate to others, and then how we influence others, and so on…
Employing weapons such as the Jo and Bokken in training helps to illustrate and magnify the central principles of Aikido by changing the Maai -- the movement is made larger and more idealized.
Of course, this is just my personal, heuristic perspective, but I hope someone finds it helpful.
Domo Arigato Gozaimashita!