I don't actually think they want to erase their own culture, because in one part they say that family will provide all the aspects of their domestic culture.
I think they want to bring up a child who will be completely at ease in the higher levels of British society. Because their background is obviously foreign I presume they think they can't do that for their child themselves, so they want to employ someone with that background to teach the child the subtle nuance, cultural capital, manners, social etiquette etc of that level of British society from a very young age so the child develops the accent, manners, social background etc to feel absolutely at ease.
I can see why they would want to do that because it will benefit the child, but I'm not sure why they've already written off the poor 5 year old. Maybe he speaks with a bit of a London accent because they didn't get an RP speaking nanny or something.
I think they see the ease with which British people of that type move through the world and think that money can buy the person to give it to their son. They are right in that the life a child has lived by the age of only 3 can influence what happens in the rest of their life so maybe they are hoping that this tutor will give their son that advantage before he goes to school.
Would be very interesting to see who they choose for this role and how the child has turned out in 25 years!