What do you think? How is it with all this education after all? . Is it mandatory or not?
Let's see the facts:
1) Satoshi, Haruka or Hikari travel all over the world and no one thinks they don't go to school.
2) Koharu normally attends school and doesn't seem to be able to drop out of school until she graduated.
3) Gou is supposed to be in school too, but he mostly accompanies Satoshi. And we have the same as in point 1, so seriously no one of the adults cares about the fact that they miss lessons?
A bit weird, don't you think?
So in the Pokemon Universe, Age 10 can be compared to ~18 (Reaching College age) in the real world, where most people get independence and are able to make the decisions they want.
1) Before this age; Trainer schools and different types of educational activities do exist for Children in the Pokemon Universe. We've seen some examples of trainer schools for this and additionally, we've also seen Ash/Goh/Serena etc take part in one of those activities with Oak etc.
2) Additionally, the most typical "Career" option would be Pokemon Battling which doesn't require an official education. Back in Kanto, I remember there being an Elite School that allows trainers to graduate and directly compete in the Indigo League. The Alternative would be to take the DIY route by figuring things out and learning to battle yourself and getting through the Gyms. I would consider Gym Badges as a type of assessment alternative to whatever assessments at the Pokemon School; they use to more or less assess the competence of a trainer before the Indigo League.
3) Finally, for specialist roles, I believe there is much more of an educational process. Outside of being a "Pokemon Trainer- Battler", for things like becoming a Doctor, Ranger, Researcher etc. There seems to be some form of education necessary to become successful in these areas.
The way I see it, you could compare Pokemon battling, contests, showcases etc (The more typical career paths for trainers), to artsy roles like Singing, Dancing, Painting etc. You could obviously be great at these things by yourself with innate talent and practice, or you could also go to prestigious academies and learn or also learn from some high credentialed officials (Like Rose offering to Coach Ash & the lady who offered to Coach Serena back in Kalos etc.)