Except with antibiotics history did not quite play out like this, in that there were far more fatal diseases before the invention of antibiotics, and some superbugs can be controlled with different variations on the same basic technology.
Sure it did. In fact, already in the 60s the original penicillin became dangerously ineffective. Around that time we (==humanity) developed semi-synthetic penicillin that enables us to change some core ingredients in the formula every few years and thus avoid saturation by bacterial evolution.
Of course, IANABiologist, so look for more information if it interests you.
p.s. if anyone is around London I highly recommend going to the Alexander Fleming museum. Highly recommended and since (sadly) no one goes there you effectively get a private tour of Fleming's lab.