Library bonuses can save us AP by letting us succeed on actions we'd otherwise fail at, or get us rewards that themselves would be worth spending AP on. I think you can understand that latter sentiment given that you're willing to spend an AP on an upgrade to the tower.
So, now that I'm at home behind an actual keyboard. Here are my reasons why I think your idea of "we have infinite money because we can infiltrate ourselves into an enemy base by spending AP and get loot" is not a good one, and why for you
@Glau why the adventures with Gretel and Johann rate near the bottom of things I want to do.
We don't have to. An influx of money is already in our future whenever we next infiltrate any of our enemies as part of the next war turn we undertake, because going by example they will have currency we care about that we can simply choose to take. This takes no AP out of our main turns because war turns are interludes with their own action limits. It certainly cost us basically nothing to gain all that Skaven loot, except risk to our limbs and that risk never went sour.
I thus see actions of "go out and get money on our time and dime" to be unnecessary.
In response to this quote directly, the Library basically had nothing to do with the tower or giving us extra rewards because it is marginal bonus farming. I see it as extremely unlikely to generate rewards that are worth AP, and so spending AP on getting resources to expand it is just throwing AP down a hole. I am willing to spend an AP on a tower because of the very large effect it has on the safety and feeling of safety for every halfling, human and dwarf living in Karak Eight Peaks and consider it strategically vital.
In terms of library purchases I am of the firm opinion we can sustain piecemeal purchases of books on specific topics we anticipate needing to do with the bulk of cash we have and our income. 322 silver ingots at 3.9 crowns per ingot is 1255.8 imperial crowns spent freely, and we can finagle "for the benefit of the Karaz Ankor" by selling "to short bearded fellows" so we can and have been applying the Karaz Ankor cash which at this point is 455 at 3.9 imperial crowns for 1774.5 imperial crowns. We also have our stipend as a councilor that has us currently sitting at 285 K8P gold coins or at 3 dwarven coins to 3.9 imperial crowns 370.5 imperial crowns. With 255 Stirlandian gold coins.
Our total hoard in Imperial Crowns is worth 3655.8 imperial crowns. That can easily withstand 300 gc purchases and less long enough for the EIC debt to pay itself off in seven turns and then we start pulling in 125 gc a turn. 300 is enough for +1 base, +1 Extensive, and the +3 from Esoteric if we want to fork over the Favor and still have 50 left over. Most topics we don't want to spend Favor on, so that can 300 gc can buy Extensive in three different subjects.
We have the money to do things piecemeal and topics only enter relevancy in piecemeal, so we should buy piecemeal.
Finally as to your proposed topics I have this to comment as a final note on why I wouldn't buy it even if we had infinite money:
Extensive Dwarven Enchantment. Vaguely useful.
Extensive Bretonnian Ranald. Don't need it, Theurgy is a ways off.
Extensive Bretonnian Arthropods. Don't need it, the We aren't benefiting from our library while we're teaching with imported teachers and we got one that seems to be working.
Esoteric Imperial The Karaz Ankor. Might need it for Belegar.
Extensive Bretonnian The Karaz Ankor. Might need it for Belegar.
Extensive Esoteric Imperial Geography. Don't need it.
Extensive Bretonnian Geography. Don't need it.
Extensive Esoteric Imperial Mutants. Useful for living organism research.
Extensive Dwarven Mutants. Useful for living organism research.
Extensive Bretonnian Mutants. Useful for living organism research.
Extensive Esoteric Imperial Guns. Vaguely useful, we're only peripherally involved with Johann or Max's gun work.
Extensive Dwarven Guns. Vaguely useful, we're only peripherally involved with Johann or Max's gun work.
Extensive Bretonnian Guns. Don't need it, they hate guns too good luck getting anything worth our money.
Extensive Bretonnian Canines. Vaguely useful.
Out of these only mutation is directly and actionably useful to our most prominent research plans.
How useful the Karaz Ankor depends on how much Belegar needs our help after the Tower of Doom went up.
Five book purchases out of fourteen is not a ratio I want to vote on. I like our library expanding because the narrative of Mathilde accumulating the largest collection of tomes outside the Imperial Colleges and in the Border Princes is very cute, mystical and hilarious when its full of things she picked up here and there as "ooh I'm working on that soon!" and very much not when its "Lets spend half my dosh on a splurge of topics".
...I just realized something terrible.
We need to figure out how to arrange for Malekith's death, stat.
How are we supposed to show our face to Algard after this turn otherwise?
Tell Morathi he's cheating on her with the Imperial Empress using the Deceiver?
At least I can corroborate this hypothesis. You might say that it's a great portion of my overall desire for most forms of fame and recognition.
Become celebrated by the populace? Headpats from the people of the empire. Be acknowledged by the emperor? Headpats from the nobility. Have everybody in the Gray college treating us nicely and clearing us for battle magic because they like us so much? Scholarly headpats from our friends and equals. Have King Belegar offer us a home in Angrund halls, or Kragg the Grimm listen when we start talking and call it good work? Proper dwarven headpatting techniques, honed for centuries. When we do something we think somebody would like, we come back around to them to show off, not to rub it in their face, but so that maybe they acknowledge their gratefulness and indicate that they like us: Headpats from those we assist.
If you'd like to put it in IC terms, I'd say it might have had something to do with Mathilde getting told all through her apprenticeship that Grey Wizards almost never got the credit for stuff. That it was a thankless job and the only satisfaction we'd get from most of it was a job well done, because the vast majority of the time nobody would ever know what we'd done. And then we went to Stirland, and got to have a taste of that not being the case. As the spymaster most of what we did was surreptitious, but we still got to have a reputation, complete with fancy title. Mathilde learned the truth; it was perfectly possible to be a grey wizard and get the headpats too. Maybe not in the moment, but afterwards, when everything's been hashed out, the people who are nice to us might still give us the credit. My tenses fluctuated a little there.
And more evidence that Mathilde is a cat gets added to the vault.
E: Oh yes voting.
[+] The Wizards of Karak Eight Peaks (locked in)
[X] King Belegar, to try to get some idea of where he's at with his crisis of faith.
[X] Prince Gotri, who is enhancing the underground defences of the Karak.
[X] Princess Edda, to pry for details about her illicit romance with Prince Kazrik.
[X] Princess Edda, on a hunt for weavers across the Empire.
[X] Prince Kazrik, as he tries to convince Nuln to let him make them fabulously rich.
[X] Gunnars, to see if you can pierce his terse nature.
[X] Oswald Oswaldson, newly-minted Chief Bombardier of the Undumgi
[X] Algard, reporting the Skaven Civil War in person instead of in writing.
[X] Empress 'Heidi', to be present for the birth of her child
[X] Yes. What better place to burn armies from than the skull of a dragon?
Because holy shit that is a bitchin control throne.