Mary and Frodo made the choice of public school based on ensuring the kids would mix with the 'right' children (i.e. wealthy). There was no - AFAIK - consideration of the kids' interests and capabilities.
Given alot of the DRF's holidays and assets are paid for by benefactors, it's never too early for the kids to mix with the people who will pay for their holidays / life in the future.
I'd like to add that I believe that in Christian's case that the school, faculty and students were selected because they'd be the best fit for him and his educational/behavioral needs. As Maria and other Danish posters have pointed out, the class stays together for years which is unlike most American schools in which we will shift groups from year to year.
If Fred had had a better experience at Krebs and if they had been able to meet Christian's needs then I do believe Mary and Fred would have considered that school for its student population.