Male Mithra(the cat race from FFXI) did indeed stay home and take care of the kittens. the one we DID see was mobbed for attention.

As for the Padjal, They're Hyur who have been blessed by the Elementals to act as intermediaries for the rest of the nation and to be its de facto leaders. It's canon that most of them keep to the deepest part of the Shroud in their own village. If I recall correctly, the majority of them spend their time calming the lesser spirits, Kan-E and the rest of her contingent left the village as moral support to the city-state so a representative of the leaders of the nation would be on hand.

Side note that I never tire of trotting out: the Conjurer trainer is actually older than Kan-E by a wide margin, but gave the leadership position to her since she looks older.