In your games, do you consider that each and every single member of a Clan attend a school? What about the guards or Ji samurai of a remote castle in a valley. May be no Dojo there, if the lord can't afford to maintain one. So probably can't afford either to send all his retainers to be trained. Maybe his sons will be, as he was.
I consider than less than 60% of a Clan are actually schooled. The proportion of schooled individuals is higher in Cities, large castles and wealthy holdings.
Those not schooled would still have skills, maybe were taught a few Kata by an older sempai. But school secrets are for gifted or privileged individuals.
Edited by Nitenman