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1. Monstrum says that in order to get rid of witchers Kaer Morhen must be destroyed
2. The battle that ensued after wide distribution of the Monstrum wiped nearly all witchers. It would not be possible if there were more Kaer Morhens elsewhere
3. Even when we get to part where other Schools are mentioned Kaer Morhen is the only place of relative safety for witchers.
4. Indirect mentions of the Keep also are in the context of it being the only source.

1. Monstrum says that in order to get rid of witchers Kaer Morhen must be destroyed
2. The battle that ensued after wide distribution of the Monstrum wiped nearly all witchers. It would not be possible if there were more Kaer Morhens elsewhere
3. Even when we get to part where other Schools witchers are mentioned Kaer Morhen is the only place of relative safety for witchers. What's more - those witchers, calling themselves Cats, are known to be failed mutations, defective both from the point of the Trials and in the meaning of true witcher (defender of humanity against the monsters)
4. Indirect mentions of the Keep also are in the context of it being the only source
5. From the bit where Triss contemplates the witchers training and diet of Ciri one can also infer (but this is by no means anything more) that Kaer Morhen area is the place of prevalence of organisms not seen elsewhere, and which are crucial in the forming of the witcher.

EDIT 2:

And I have to retract the statement made elsewhere that Season of Storms says that Kaer Morhen is the source. Book states who made witchers, not where. Damn and blast the fragilis of my memoriam... So I'm clearing that up.

Can I stop now?

EDIT:

The conclusion of all those excerpts is that nowhere - up until Season of Storm - it's mentioned that there are multiple Schools. We have only faintest hints in form of witchers' medallions in different shapes, but that's that. Also, every time when Kaer Morhen is mentioned, every person knows it was the home and source of witchers, including magi who knows best (again, as mentioned in Season of Storms), as opposed to a home. In short: multiple Schools as we know them are the game concept only - books mentions only one, in connection with just one other witcher, and there's actually not much more than that. In contrast, the information on the uniqueness of Kaer Morhen is as follows:

1. Monstrum says that in order to get rid of witchers Kaer Morhen must be destroyed
2. The battle that ensued after wide distribution of the Monstrum wiped nearly all witchers. It would not be possible if there were more Kaer Morhens elsewhere
3. Even when we get to part where other Schools are mentioned Kaer Morhen is the only place of relative safety for witchers.
4. Indirect mentions of the Keep also are in the context of it being the only source.