I enjoy seeing her appear too. She has such a fun and interesting personality. I think she appreciates Hazou's honesty and that his mind, with all his lists, works similarly to hers (however the Frozen Skein interacts with her).
I think what it comes down to, in the end, is trust. We can't trust her with things because, as you pointed out, she has her secret goal. Furthermore, she's as clear as mud to us whereas she seems to know what we want and how we're going to act. Adding in the fact that she's a jonin and ostensibly loyal to Mist first and we can't afford to truly bring her in until we've either leveled socials or found out enough information to understand her.
I'm 100% down for including Ami more in things, but we should definitely keep them as low priority things that she can't do anything with, such as the one salt making trip we took with Naruto. Hard to make an OPSEC mistake with straightforward, low-priority objectives.
You know, I've been thinking about the subject of trust lately. Mostly because of Keiko's revelation that she's part of an Illuminati group dedicated to preserving the world and guarding it from malicious Outer Beings that have been sealed away. Keiko has other obligations, other responsibilities, and one day may need to betray our trust as a result. However, knowing Keiko as we do, we know that she would never,
ever, do such a thing lightly. And she would only ever do it if were the only option, or if it were legitimately the best option. Like Hazou said, "trust can be rebuilt."
I
think that we can trust Ami, at least with the less valuable op-sec stuff. We know her well enough to know that she's on our side, and that we're her friend and that she's ours --well, as we define the term, rather than how she defines it. Knowing what we do about her, I think that we can safely assume her Ultimate Goal is at least somewhat benevolent, especially since it doesn't openly contradict Uplift.
At some point I'd like to do two things along these lines. 1) ask Keiko if Ami can be trusted. To ask Keiko to take a mental step back and, objectively, give us her opinion on this. We might also want to ask Snowflake, if only because it would make the scene that much more interesting. 2) tell Ami what we told Mari,
minus our deductions about the Forbidden Five. That the very fabric of reality is an existential threat to humanity and that, if something isn't done, our species will eventually be thanos'd. On the off chance that she doesn't already know, we get an ally against the Out. If she already does, then we still get an ally against the Out. Existential (or would it be ontological, in the case of the Out?) Threats are great for uniting people.
And it's worth mentioning Ami is very much NOT on the side of the Mori, so even if she deduces that we know about the Forbidden Five, I find it
very unlikely that she'll try and go after us for it. She knows that we're on the same side because, if nothing else, uncaging an Outer Entity would also burn Uplift to the ground.
Besides, Yuno knew and she only seemed to get a very,
very stern talking to about op-sec from the Nara, who are actually allied with the Mori in more than name.