BS”D
Neither Chazal nor anyone else dropped the ball on the cure for cancer. Hashem for whatever reason has not yet revealed the cure for malignant illness.
The Rambam was most probably a far greater doctor and certainly far more intelligent and righteous than the discoverer of penicillin (Fleming?). For one thing, the Rambam spoke of aerobic exercise and dietary restraint when people believed in resting and overeating.
But Hashem instead decided to reveal penicillin, a mold that existed since the beginning of time, to a non-Jew who was not even looking to mold as an antibiotic, but who somehow chose not to throw out his moldy petri dish. The penicillin was there, but it was Hashem Who decided how and when to reveal it.
And He did so during World War 2, to a British scientist who was charged with preventing infections in soldiers who were wounded while stopping the most vicious tzoirer ha-Yehudim of all times yemach shmo.
When the Rofe Koil Bosor decides to reveal the cure for cancer, it will come. It could come bederech hateva, in a university or drug company lab (and if in EY this might be bederech Teva, but their R&D is actually very overrated), or it could come out of nowhere, for instance from someone noticing some effect on cell growth when he spills food or cleaning solution in a test tube.
One thing is for sure, looking for ways to reduce the niflois haBorei to mere mundane chemical occurrences and to otherwise dray Torah chas vesholom is not going to draw down the siyata deShmaya that is needed for this cure to be revealed, even if Hashem reveals it through an oived avoido zoro in the Far East.