It seems like Kano could've easily gone a different direction and focused on striking, weapons, or even a general sport. Why did he have such a keen focus on grappling in particular?
On Modern jujitsu by Tomiki, Kenji there is a nice diagram (see below) that explains the evolution of old style jujitsu, striking arts, and weapon arts into modern budo practices. In this paper, we have a quote from Kano-sensei from 1926 about past and future judo:
I think that there must be a method of randori and shiai that includes the atemi-waza, provided that we devise it gradually and only after thorough investigation. That system, however, is not as easy as the ones in which the relative merits are decided by throwing (nage) or restraining (osae) an opponent.
This, along hints within the rest of the article, seems to point that safe competition was a (the?) factor that pushed Kano-sensei to move into the close grappling range.
Kano wanted to make his Judo system something that could be done at full speed and force yet which did not seriously injure anyone. He realized that only this way could people continue to make progress over time, and it was this personal progress - building character along with skill as a result of continuous effort over time - that became Judo's focus. That was Kano's number one guiding principle when founding Judo.
And it's obviously true. You can't come back tomorrow if in training today you get broken bones, sprained limbs, and popped joints.
At the time, this was counter to the prevailing attitudes and philosophies of his contemporaries teaching jujitsu. They all had the idea that you couldn't even do randori (sparring), because the techniques were too deadly. People would get seriously hurt. So they didn't even try. Instead, they limited their focus of practice to solo and partnered kata and drills.
What we call "jujitsu" today was, back then, various Samurai "ryu" (clans). Each ryu had collections of techniques involving throws, joint locks, submissions, striking with the hands, striking with the feet, and weapons such as sword, staff, bladed chain, rope binding, knife, spear, bow-and-arrow, etc. Some ryu specialized in grappling, others specialized in sword and other things, but they all had broad knowledge of the other aspects of self-defense and warfare. (And actually, the focus of most of the older ryu was warfare, not self-defense, and so sword, spear, bow-and-arrow, etc. were often much more developed than their grappling was.)
Kano took the grappling techniques and some striking kata of different Japanese ryu which specialized in grappling to make Judo. But he never was able to incorporate striking into randori, because there was simply no way to practice it at full speed and power without people getting hurt. That would be a necessary requirement before being incorporated into his randori.
And what role striking would play in Judo randori was also uncertain. Was striking merely supposed to be used to help unbalance or distract opponents? Or would points be awarded for strikes along the same lines that they are awarded for throws?
So striking didn't fit in nicely into Judo randori. I imagine Kano contemplated limiting striking to certain techniques that would not cause as much damage, such as an open palm strike to the chest or a slap to the face, similar to Sumo wrestling. He might have even played with this with his senior students. But for whatever reason, he wasn't able to merge the striking into his grappling randori.
Of course now we have Brazilian Jiujitsu, which incorporates strikes into a system of techniques that derives primarily from Judo. But even BJJ does not permit strikes during competition. For that, you go to the next evolution, which is MMA. But while it's possible to "spar" in MMA and not get hurt, you won't be as lucky when you go all-out in actual MMA competition.
So as far as I'm concerned, nobody including Kano has been able to incorporate striking, at full speed and force, with grappling safely. If it's just sparring (light to medium force)? Yes, that can be done successfully. With full speed and force? No. The same level of control as grappling just isn't there with striking.