No, the common stuff needs medicine to. Obviously the biggest thing 'common' illnesses need is to be prevented by our ever expanding array of vaccinations, which is why you now think of 'common' as synonymous with 'mild', because smallpox, strep pneumo, and diphtheria aren't common illnesses any more. Flu would be a lot less common if that vaccine was mandatory.
That being said even common illnesses often benefit from medical interventions. In childhood antifungals for a candidial diaper rash, antibiotics for strep/UTIs/Otitis media and Zofran for vomiting are extremely effective interventions. Misery doesn't need to be life threatening us to fix it. Nothing really works for cough yet, but then again 10 years ago nothing really worked that well for vomiting and then someone invented Zofran. For common conditions of old age I wouldn't want to have to get old without the option for joint replacements for my knee pain, artificial lens implants for my cataracts, and Lasix for my hypertension. And of course almost all of the common conditions of mental health, from depression to inattention, improve dramatically with medical management. Natropathy does nothing for these illnesses other than misdirect patients who could have been fixed if they found their way to a real doctor.
Even when common illnesses are beyond the reach of modern medicine, what they still do not need is quackery. They don't need Vitamin C, ginsing, acupuncture, Reiki, or naturopathy. They don' t need them because they don't work and no one needs to be robbed of their money in exchange for nothing. They also don't need them because patients need to understand the limits of medicine to get back to their lives. Patients who have some kind of medical misery tend to assume to role of 'patient' until you either fix them or they accept the fact that they can't be fixed. Obviously the fun part of medicine is fixing the fixable patients, but the noblest part of medicine is having the strength to look a patient in the eyes and tell them that there is nothing that you, or anyone, can do. That's true whether its a mid common illness like bronchitis or an inevitably fatal condition like metastatic pancreatic cancer.