Ultramar is not going to be a problem. If the Destroyer doesn't arise they'll be put on the backfoot by the Taus AI advantage and desperate to catch up, if the Destroyer does arise they will be fighting alongside AI-forces for an extended time, diminishing prejudice. They are the most likely to want a piece of our MoS in my opinion. In fact, if we don't give it to them they'll probably develop their own by reverse engineering Tau examples.
Ultramar has been fighting against the Tau and their proto AI for a very long time and are still by far the most xenophobic polity out of the big three to say nothing of the fact that against the Tau and the Necronish destroyer, AI of their own is possibly most likely to cause issues.
Far from guaranteed, but still.
Logic does not truly matter after a certain point.
Ironic or a people that prides itself on being logical.
I think that Doomed Wombat and Enjou are both focusing on the wrong thing when it comes to why our psyker knowledge is not very useful to the other powers. It is not that they can't learn it, it is a problem of why would they?
All the other powers have, on a per capita basis, massively less psykers than the Trust, and over the thousand years since that Fall have worked to find the niche that is the most useful for their psykers to fill.
Why would a Callamus Psyker tech priest care about Biomancy? What the use of training how to form a chorus when you are never going to have enough psykers at the same place to use one? We have been growing our psyker knowledge in a direction that makes the best use of our absurd numbers, numbers that the other powers just don't have.
We face a similar problem with establishing our psyker orders, if we only had enough psykers for two orders we would not bother with any power research outside of those two.
Farther more, Durin already said that they will be making use of our knowledge, "not very useful" is massively different than "of no use at all". If a given power is applicable than it will be integrated, if it is just so good that it is worth learning anyway, than they will learn it anyway.
Well lets look at what we know, Midgard produces an extremely large number of psykers, not as many as Avernus no, but still an extremely high number none the less.
I think we can take that as an average for the human species, if not below average since we skipped 1000 years then how many non trained psykers do you think the big three produce with hundreds of hive worlds a piece?
Quartius specialises in its Librarians Callamus in Tech Psykers and secundus can't actually get theirs so forgive me for assuming that there's a probably a large number of untrained normal psykers who represent an untapped resource.
And no they will have enough psykers for choires if the bloody Imperium was creating psyker regiments by the end of its existence then I can guarnatee their numbers are not so low that they can't make a proper choir if nothing else out of Librarians.
The thing is that hypothetical isn't a reality. They won't be able to do research that's why we have Avernus, we can do the research for the regular psyker orders.
But to answer your hypothetical I'd have thought learning more about the nature of the warp in general and researching outside of those two fields would be rather fucking important if for no other reason than to improve and adapt their arsenals in the face of the overwhelming piles of chaos psykers and daemons! But apparently this is not the fucking case, because its how they do things.
Not very useful means not very useful. Its only slightly better than of no use at all, and if all we have now is not very useful then its going to continue to be not very useful whether its the powers we reverse engineer or the fundamental nature of the warp we figure out.