Now, I'll admit that I'm very skeptical of the idea that Mountain is a resource that we can lay claim to (maybe if Ami marries in and we have her do it, which is its own kind of dangerous), but something I want to head off:
I generaly agree to what you say in the post, but I have arguments against this exact sentence: it should be Gouketsu's influence, not Leaf's. Even if Jiraiya manages to solidify his claim to the hat, the next Hokage can come from opposing party. In this case all Mountain resources gonna fall in wrong hands. If the influence is of Gouketsu, than our assets are more secure.
This is very dangerous. If Jiraiya loses the hat, then the surface reason may be that he has too many other responsibilities or someone else has closer ties to Leaf's ruling powers (due to his time away as spymaster) or because they say they want him able to act away from Leaf, but at least some of it's going to be because he took in four ninja who were
definitely never missing-nin (we promise!). Securing an entire separate and very visible power base plays into that narrative, and in a way that can be utilized to basically concern-troll. It's openly aggressive and very impolite to say, "should we be worried about the fact that the guy we just replaced as temporary Hokage is keeping a personal grip on this secret ninja village? what's he planning to do with it?" It is, however, socially accepted to say, "well,
I know that the honorable Jiraiya of the Sannin has no ill intentions, but this looks bad, doesn't it?" And if you repeat that often enough, that sticks in people's mind even if no one takes an open stand against it.
(This can't be done with the "adopting missing nin" thing, because of the polite fiction that Team Uplift defected to Leaf from the very beginning. Calling them "missing nin" with the usual connotations of "disloyal and scary" is an open challenge to Jiraiya, so you can't concern-troll and still maintain plausible deniability.)
You should ask yourself: are you willing to let Leaf have the resources, even if Jiraiya loses the hat? If you are, sure, go ahead and act. If not, then you should advocate for hanging back and not securing ties to Mountain until you're sure Jiraiya has the hat secure--
but be aware that Jiraiya's stated opinion on such matters is that Leaf always comes first for him, and that advocating for this course (even quietly and discreetly) will likely not be received well. So if you want the resources for Goketsu and Goketsu alone, it's a good idea to stay away from Mountain until the matter of the hat is resolved, so as to try and ensure that the issue never comes up at all.
