No, this reuse was not intended, of course, but it was often practised within the family.
I don't know how well you know the period, but in general you can say that many people were really poor at the beginning of the 1930s. That means: never taking a holiday, struggling to pay the rent and utilities, scarce food, working 6 days a week (if you had one, otherwise the welfare wasn't even enough to get by). That's how it was for many back then. And so it goes without saying that savings were made wherever possible. This also applied to the children's civilian clothing, and even more so to the expensive uniforms. If a family had several children and a complete outfit easily cost half a month's salary, that is not surprising.
The ready-made uniform shirts came in 10 different sizes.