They don't know.
Mostly they have no idea if the person in scrubs from anesthesia is a doctor or nurse.
They aren't informed and don't understand the differences.
They aren't given the choice.
They're brainwashed by the media to worship those kind, caring, overworked, dedicated nurses, and to resent those greedy, arrogant, inattentive doctors.
Patients are the last people on earth who should be asked about the quality of the healthcare offered to them. Good care to a layperson is a "provider" who smiles at them, magazines less than a year old in the waiting room[1], and zero wait times. They don't know if they're getting the right antibiotic, if their kid's asthma is being managed optimally, or if the person aneathetizing them is going to let their systolic BP slouch at 71 for 20 minutes while waiting for surgical stimulation.
[1] in the pre-smartphone era, anyway, now nobody reads magazines