the thing is, most children are actually fairly similar to their parents in terms of abilities. Not always of course but if you have two parents who value academics, your normal life will be galleries, exhibitions, museums, chat at dinner about world events, books, theatre etc. Not in a snobby way, just that’s your life.
If your life is business and sport, that’s your life - so sports events, galas, shopping, talk at dinner about those things. And I think in general at quite hard to move between those worlds without quite a lot of effort.
Even going to a great school can’t infuse all the other things. So if in the school holidays the Beckhams are going along to sports events, talking about sport, fashion etc, then that’s understandably what they’re likely to take an interest in.
Plus if you’re so rich that you never need to worry about money, and you’re not particularly academic, it would be hard to insist on chemistry homework being completed when you know full well your kids are not likely to be a scientist.