Eating properly and exercising and general healthy living is a must. That alone will cut down disease rates significantly. I myself, when I started following a healthy lifestyle, didn't get sick for ~2 years. I got sick again last winter and it was like a trip down memory lane: I was like "oh, yeah, this is what it feels like!" Instead of feeling down I was very keen on examining every single sensation!
And yeah, once you get sick, you should let the disease follow its natural course. Yes it might take 2 weeks for you to feel tip-top again, but taking antibiotics in a hair-trigger manner is gonna be worse in the long run, and for people in general, not just you: taking antibiotics is a public act, not a private one, much like smoking.
But why do people do it? I don't think their reluctance to suffer through the disease is the number one reason. I think the number one reason is their jobs. For poor people especially, in the U.S., missing just one day might get you fired. So people do whatever it takes to just keep the machine running. That's why everything is interconnected: if you want to fight antibiotic resistance, you can't just concentrate on that one single issue, everything else must also be improved. That's often something people fail to realize, how every single thing affects every other.
Anyway, those are my two cents!