I believe that in its origin, the Ministry School was invented in the WW2 years to support the WT claim that all JWs (men only at first) were ministers and could then get classified (ie: Qualified to be Ministers) as a minister and thus get draft exemption. In the Walsh case they presented this argument to support their stand. There was even a written exam for a time.
The 'school' has morphed into something else over the years, but I think that was the original impetus to introduce it into the weekly meetings.