Your nanny will be around 2500/mo - down to 15.5k
Your 600k house will be around 4300/mo - down to 11k
Malpractice insurance / practice fees is anyones guess but lets be reasonable and say 2k/mo - down to 9k
So were down to saving 9k per month but then there is all the other stuff, food, electricity, entertainment, kid expenses, clothes, etc etc. Id say this usually amounts to about 3-4.5k per month ($100-150 per day) for someone who expects to live decently well.
Anyhow nobody is going broke in this scenario but our rich dermatologist is "only" saving 4-6k per month amounting to about 50-70k per year. Not horrible but not the extravagant wealth that you might expect. Note that I was also pretty nice to our hypothetical doctor - in this scenario they dont even have any student loans or a fancy car.