There are several reasons why a shitty training centre makes foreign teachers or "teachers" work on an F visa:

- They are not licensed to hire foreigners because they do not qualify.
- They are an illegal "school".
- They are too stupid to know how they should proceed with supplying a regular Z visa.
- They are too lazy to follow the proper procedure, etc.

All that is just fine with me, as long as they don't get lazy paying me, and treat me well, then life is rosy. they can lock students in the broom cupboard and beat them every day, as long as they pay me.