If docs didn't slot 15 minutes per patient, then they would need to charge each patient much, much more or make much, much less. There is no other way around that.
I'm willing to bet that something to relieve the massive amount of "other" stuff needed besides the Doctor would go a LOOOOOONG way...
That doesn't even tackle stuff like inability to see how much something actually costs - and shop around for stuff other than the ER.
15 minutes per patient isn't the answer...