Because the instruction from most pediatricians is to send kids with persistent (not responsive to acetaminophen and/or ice bath) fever above 104F to the ER, especially after hours. Very, very rarely will you find a pediatrician available outside an ER setting after hours.

Yes this is right

Doctors make up 11% of heathcare costs in the US. Their bloated salaries probably contribute about 5% to total costs. Its not insignificant.

Most doctors are scheduled out for weeks. Best bet is an urgent care/walk in clinic. (Good luck if they have a pediatrician.)