I think it's worth noting that jō is sometimes translated to English as "cane". While it doesn't match up in shape and size to a classic European cane, it does match in purpose.
Another interesting fact about the jō is that it's also the size of the haft of a farmer's spear: in the feudal period of Japan, a commoner couldn't keep a full-length yari, but was permitted to keep a shorter spear for purposes of self-defense against bandits and the like. Much like a yari, a short-spear would also commonly have a blade end and a spike end, so double-sided movements work for both spear and staff. There's still a few sensei's who will train Aikido-spear (Aikisō), but it's uncommon.
Ueshiba Ō-Sensei was captured on film on several occasions performing all or part of a short-spear kata called "Nuhoko" or "Nuboko" (meaning "jeweled spear"), however, in the vast majority of the film clips, he is using a jō.
While I suppose Ō-Sensei could have drawn some inspiration from Shintō Musō-ryū, Aikido's jō techniques, as taught by leading Shihans (notably: Saito, Saotome, and Chiba), look quite distinct from MSR.