Here the problem is rather not in the science and development of medicine and modern technologies, but in something completely different.
I am more than sure that for a long time there have been more or less effective drugs for cancer, AIDS and many other similar diseases, but for someone it is simply not profitable for the world to know about them.
Modern medicine is also a huge, powerful business, which also has influential people who can easily shut the mouths of too smart guys who can invent a cheap and effective elixir against diseases, to get rid of which thousands of people spend millions ...
What will happen if such an expensive treatment can be replaced with one cheap or at least just less expensive pill? A huge system will collapse, and under it will be buried the capitals of many very rich and influential, who now and, perhaps for a long time to come, will do everything to keep everything in this world in its place. Even at the cost of the lives of thousands of sick people.
Naturally, he can. The only question is whether we will be as lucky as with antibiotics when their discovery was sudden, or whether we will have to go a long way to synthesize drugs through repeated trial and error. In the first case, a quick victory and complete defeat of the enemy, in the second - an invaluable experience that will allow solving medical problems of the future.
I'm not an expert in virology and medicine in general, but once I read the opinion of a modern Western philosopher. So he expressed the opinion that diseases of this type - incurable at this stage of the development of science and medicine in particular - are the reaction of nature to some kind of disruption in the development of mankind. And he gave, for example, cases when animals of a certain type, whales or dolphins, for example, died en masse. Or when plague mowed down half of Europe. And now these diseases have arisen against the background of aggravation of problems in society around the world. At the same time, these diseases like cancer or AIDS or plague in early times are just a tool with which nature "tailors" us. And if a cure for the same plague had not been found in due time, then there would be no AIDS or cancer. The tool would remain the same.
Quite a strange question. If humanity does not destroy itself earlier, then sooner or later progress in nanotechnology will allow for a complete debugging of the human body. Tiny machines will audit the cells of the human body and simply kill cancer cells, repair DNA damage, restore the immune system (how it will react to an army of robots is another, also interesting question). Stupidly in the forehead, due to the increased technological power, humanity is able to defeat these diseases. The question is, when will these miracles become available to even not mere mortals? Progress in science, as already noted here, is extremely unpredictable.