"Maybe there should be a standard placebo 'antibiotic' for these cases"
It's an interesting idea, but ethically dubious. Your doctor would have to lie to you when prescribing the placebo because (s)he would obviously know it's a sugar pill. This applies to all prescriptions of placebos, not just here. Having your doctor lie to you, even if it's in your own and society's interests erodes the trust that should exist between the two parties.
Once this "got out" that "apoxylalacillin" is a placebo there would be a backlash against the medical profession, claims of "big pharma" conspiracies, and possibly the movement of people away from medicine and towards alternative therapies because "doctors lie about medicines". Now the latter is fine if it's a self-correcting problem like a cold, but could be fatal if the patient had a serious condition that really wasn't going to be helped by a nice cup of herb tea and a dangling crystal.
Education has to be part of the solution. The general lack of knowledge of basic medical matters is appalling. I'm not advocating that everyone should be a doctor, just that there must be room on the curriculum somewhere to teach about antibiotics, anti-virals, why most drugs will not resolve the problem instantly, why to always finish the dose of any drug course, how to deal with simple injuries, why going to casualty with athlete's foot is a dumb idea etc. etc.
there also needs to be support for doctors refusing to prescribe where it is not necessary. Maybe upon refusal to prescribe the patient is given a form where the doctor writes on it "viral infection, no suitable medication" and the patient can send it off as a complaint. The patient then gets back from NHS Complaints Central a letter saying that no prescription would help, and have they noticed how they now feel better as their very own immune system has sorted it out.