Interesting to compare with how the UK army approaches training. Simplifying somewhat, it has dedicated schools that do trade-training for specific categories of soldiers (e.g. infantry, armour, artillery, etc). Soldiers go to these after basic training (how to be a generic soldier) when they have chosen their military specialisation. They then return as they go through career progression to do trade-specific professional development (e.g. going from tank driver, to gunner, to commander, etc).
Crucially, as soldiers (non-commissioned) go up through their rank structure (corporal, sergeant, etc) they can take instructor courses back at the schools that qualify them to do on-the-job training back in their parent units (and which increase their pay). The best of these instructors may be invited to undergo additional training that qualifies them to become an instructor at one of the schools. So some responsibility for training is fundamentally baked in to career development.