Why do you think the Norwich mage family is so "generous" with adoptions and gifting money? Are they just like Weins who is rich enough to blow cash frivolously?
I think I need to start this one by establishing who are the Norwichs.
The Norwich family is first introduced in Clock Tower 2014 through a character named only "Mrs. Norwich", who serves as a character for our protagonist Lev Lainur Flauros.
The ultimate twist of the story is that Lev Uvall, Lainur Gusion, and Mr. Flauros are three different personas of the same man, and the narrative spends most of its time showcasing the personalities of Lev Uvall and Lainur Guison, while the Mr. Flauros personality later becomes a major character in Fate/Grand Order.
Lev Uvall is the persona who values the past, a purely theoretical mage who spends his every moment of activity deciphering old grimoires, rewriting them in modern terms, and intersecting their contents with the previous texts he deciphered.
In contrast, Lainur Gusion is the persona who values the future. He's not a research-minded mage to any extent, but he's devoted to his family mission, carried out through generations of Gusions, of giving the future what it needs to prosper. His Imaginary Number magecraft allows him to create space pockets to store money, items, and papers for the future where they will be truly needed, but that's not the main way he contributes to the future. The Lainur persona spends his every moment of activity looking for talented youths under less fortunate financial or political circumstances and, through anonymous donations, providing them with the cash and project ideas they need to live up to their potential. When asked what he expects to achieve by constantly making doing these lavish donations to promising strangers, he says he doesn't know. His devotion to the future doesn't include knowing what shape the future will take. He just wants to give it every chance it can have to prosper.
Later in Case Files, the Norwich family plays a part in the background of the Adashino siblings, and later its material books goes over what the "family" actually is.
The mats explain that Mr. Norwich is anonymous donor who looks for talented youths under less fortunate financial or political circumstances and provides them with the cash they need to live up to their potential. Sanda's phrasing in the material book uses sentences lifted straight from the Lainur sections of Clock Tower 2015 to really hammer in the point that Lainur is the anonymous benefactor.
People backed by Mr. Norwich are encouraged to adopt the Norwich surname, so the Clock Tower is full of people from that "family" despite there being no real blood lineage carrying the Norwich name. Obviously, considering Mr. Norwich is anonymous, the original lineage of benefactors can't carry the Norwich name, as we see that Lainur doesn't.
The Adashino siblings also demonstrated that if you don't want to tie yourself to the Norwich name, Mr. Norwich will not give a damn. This checks out with Lainur's philosophy of enabling the future without regard to which form the future will take. Receivers are free to do whatever they want with their donation.
It's also noted Mr. Norwich of 200 years ago was the main backer for the foundation of the Department of Modern Magecraft, which tells us the Mr. Norwich anonymous donation habit as a multigenerational project. No more details since Lev is a rare example of a mage who doesn't say shit about his family. All we know is that they always did really well with money.
Ok, to the questions now. "Why are they so generous?" Because the past and present doesn't matter as long as there is still a future. Working for a prosperous future is the only thing that has value. "Are they so rich they can blow loads frivolously?" Well, technically yes, but this is not frivolous to Lainur. It's his entire life purpose.
