Instruction and Costs
You don't have to use teachers, but it gives you a great way to introduce a new NPC or bring back an existing one in a new role. The role of a teacher could also be filled by communing with the cosmos for a solarian, training with the military for the soldier, and so on. The important part is the guidance gained from that source.
Any costs to retraining by using an NPC should be pretty minor—about as much as a PC could gain by Earning Income over the same period of time. The costs are mostly there to make the training feel appropriate within the context of the story, not to consume significant amounts of the character's earnings. A teacher might volunteer to work without pay as a reward for something the character has already done or simply ask for a favor in return.