I don't know any doctor that doesn't have enough patients. Heck I can't even get into my doctor without waiting at least two weeks.
I find this question mildly offensive.
If you knew any doctors ... Or anybody in the health care industry ... Or followed news on the subject ... You would know they are overworked, and there is a shortage of health care workers.
They don't need to create more work for themselves.
The question doesn't make sense.
If a child is sick, 99.99% of parents will spend MORE time with them.