OKAY, so it's something like 2 in the morning where I live and I can't sleep. Being quarantined has my sleep cycle out of wack and I need to order more boxes before I can pack anything else up for the move. So, long story short, I was struck by the realization that Asuma's probably scared shitless right now. The first four Hokages were titans --with the Yondaime being cut down before he could really catch his stride --and Asuma's... not.
Don't get me wrong, Asuma could kill the entirety of the Goketsu ninja without breaking a sweat. But he's... just a jonin. He's not the stuff of legends like all the others (do we really count Hiashi as a Hokage, though?) and his reputation won't be enough to hold back armies like the Hashirama or the Legendary Sannin --the latter of whom are believed to be gods by some of the less educated inhabitants of the EN.
Of course, that said, Asuma's a jonin who had the Third Hokage as his father. With someone named "the Professor" and "the God of Shiobi," as a father, I'm sure Asuma's probably in the upper echelons of jonin. And we shouldn't discount the fact that he's learned how to lead from his father, even if it was only from a distance. But there's still that undeniable element of simple power that he's lacking. All of the Hokages have believed in the Will of Fire and, to the best of our knowledge, ruled by example along that path. But they were also able to corral stray elements by hook or by crook.
Asuma doesn't really have that option. More than any other Hokage before him (save for, perhaps, Hashirama) Asuma has to negotiate. He has to rely on the more intangible pressures of tradition, honor, and patriotism. The tangible power Asuma does have is of the more institutionalized sort, such as the ANBU. Things that are conferred onto a Hokage, rather than existing independent of the title. Hiruzen's personal power was such that Orochimaru fled the Leaf instead of facing the repercussions of his atrocities. Asuma simply doesn't have the personal power to do that. He's sitting on a throne, fully aware that Orochimaru or Tsunade could just... stop accepting his orders. Or else, reject Asuma as a false Hokage. Neither of them are very likely to, but they can. So that means that Asuma has to be careful with what he orders, since he can't afford to push the line too far.
Therefore, Asuma is left with one of two options: get stronger or hold the throne until Naruto --someone with practically limitless chakra, and thereby theoretically infinite personal power --can take it. And Asuma can't devote very much time to getting stronger. He's running himself ragged trying to patch the Leaf together with vastly subpar staff, maintain peace between all the political bodies, keep enemy villages at bay, run his own clan, and a thousand different other things. So Asuma doesn't have the time to do the former, and if he fails, he might even not live to do the latter.
Why don't we... help him out, just a little bit. We have a nontrivial amount of money, a river of income, and a monopoly on chocolate. And we know of a place that sells pretty unique fruits, seemingly unknown to the wider world. We also have access to a mine that we're about to set up as a mining town, right? Well. That sounds like the start of a good trade network... and when you're stuck on the road for days on end, going from place to place? Well, surely you can't help but to.... hear things.
TL;DR: Let's set up a spynetwork to help Asuma out, winning some points in his favor.