You're oversimplifying things.
It's not always easy to tell the difference between a viral and a bacterial infection. Doctors sometimes disagree with the same set of symptoms, and only a blood test can tell you for sure what you are dealing with. Often one leads to another, without an entirely clear cross over point (a bad cold becomes a sinus or chest infection, for example).
Of course over use of antibiotics is a problem. But IME, doctors telling patients to basically go away and wait to see if it gets worse is also a problem. If you end up at A & E (under huge pressure), or end up taking a needless few days off work when you get very poorly when antibiotics would have started recovery.
I speak as someone who had quite a few bouts of infectious mastitis with dc1, over 2 years of bf-ing. I got to know the symptoms and progress of infectious mastitis very well. Dealing with doctors who talked to me about blocked milk ducts etc as if I might be hearing about them for the first time, sending me away without antibiotics ("come back if it doesn't clear up" - well, I'm here BECAUSE it hasn't cleared up already) and putting me through several days of utter misery, pain and escalating illness and fever has made me very frustrated with doctors who needlessly withhold antibiotics. With antibiotics, infectious mastitis improves within hours, ime.
(not to gp bash, I should add that I found a sympathetic female doctor who bf-ed herself, and who was quite happy to give me antibiotics 'in case' I needed them. I could get them over the phone when it was hard to come in with children. Obviously I didn't take them if I didn't need them, but it was a lifesaver on a Saturday night when I got sudden symptoms and would have had to wait until Monday for even the chance of an appointment)