It's my understanding that a Feudal lord wouldn't need to travel all the way to a city in order to train in swordplay and jousting. They'd have an entourage which featured sparring partners and instructors. The idea of traveling to a city to find a swordsmaster to train with is more in keeping with renaissance and baroque fencing then it is with medieval tournament and battlefield combat.
The very idea is contrary to the cultural set up of Battle master. Why should some commoner be in such high demand that Nobles, Lords and even Kings need to travel to him for instruction? Any feudal lord of any significance should be able to hire their own private trainer.
Also I'll add that archer units don't gain you sword fighting experience. Therefore if you command an archer unit and participate actively in your realm's military then all of your skills will completely atrophy if given enough time.
The whole topic is covered in greater detail in the thread "nerf the academy" which features many concerns about game balance issues and loss of role-play potential.
Who ever said the trainers were commoners? In fact any trainer that was training nobles would almost CERTAINLY be at least of minor nobility.
The academy as is exists for game balance reasons. Tom has stated many times that he doesn't want "academy" training to be too easy, nor does he want it to be the primary way to increase skills.
