"The children of the wealthy and influential" is not an opt-in class though. Any healthy society should be resilient to 1% of its population being able to leave the workforce for their lifetime, the issue posed is what happens if 100% could.
I don't think its a concern. Most people want to work, when that work is a source of satisfaction or pride in their lives.
In line with what you were saying above, I was raised to expect to have multiple career changes in my life. What satisfies us changes as we age, and we may not have the skillset for the dominant, high-earning fields as well