Because the Sword school cuts down Samurai recruitment time starting at tier 2. At Tier 4 you are pumping out Samurai 1 turn at a time.

samurai dojo also gives me -2 katana samurai recruitment time

Ahh that should be -1 thank you.

You also get the hero unit with the original school line.

so jack of all trades vs specialized buildings?

Pretty much the point of the samurai recruitment building chain is if you want to have a region that has economic/agent buildings but still want it to be able to recruit samurai.

A major recruitment region would have several schools and the Encampment chain for whatever bonuses.