Factions & Witcher’s Cards

While analyzing Witcher Schools' Lore I found out that many of these haven't got any relation with the gwent faction they belong to.

Let's start with the Viper's Witcher School. To my mind, that is the only School which apparently suits with Lore as they closely worked with Nilfgaard, although they got fucked by the Empire afterwards.

A similar situation happens with Cat School, as they are apparently one of the few Schools training non-pureblood humans.

However, what about the Bear School? Well, according to Lore, they are located in the Amell Mountains which surprisingly are situated between Northern Realms and Nilfgaard, and not in Skellige. So, why was this School choosen to be played along with Skellige faction if they are not even related?

What are your thoughts about it?

I guess I haven't mentioned other important Witcher cards as I am a new Gwent player, so feel free to add any of these to complement the post.