First off, doing away with clinical trials as we perform them now would certainly speed up pairing drugs with patients but it's not going to happen unfortunately. Drug trials aren't designed to minimize search paths, they are designed to minimize risk.
With terminal diseases like many cancers the rules are bent a little but what's important to understand is that these are real people making the decisions ultimately. Sometimes the most information can be gained by withholding drug, and isolating another treatment's impact but if you are a patient with a terminal prognosis, or the doctor trying to treat that patient, are you going to choose not to take something that might help you?
This is a point of frustration for many in research fields because it means clinical data is hugely noisy. Patients are often cycled through different drugs quickly to find something that takes hold, while at the same time going in for as much chemo/radiation treatment as they can bare.
I'm not saying these approaches aren't relevant, they just won't happen as a grand reimagining of our drug approval system. What is starting to happen however, is reclassification of cancer 'type' based on genetic profiles meaning ovarian cancer may have certain genetic similarities to lung or pancreatic so instead of treating melanoma, you can treat a cancer with a disturbed MAP pathway.
All the same, I'm glad he's working on this problem because it's huge, and I look forward to seeing the point of view of the HN community.
edit: Though obvious to some, I should also mention this problem is complicated by the fact that genetic information is private and dissemination is highly restricted. Patients can release this info but it does often inhibit massive cross-patient research.
These drugs all fail clinical trails and are lost.
"Cancer results from finite genomic mutations that biotechnology can easily list."
Well the first part is true. The second part, not so much.
There is even the phenomenon known as Chromothripsis , which has the entire genome smashed into thousands or millions of pieces and then randomly put back together.
Perhaps colloquially, finite here is (not un-like literally) a metaphor, in this case for not-unfathomably-large, or more precisely, measurable.
Sorry to be snarky but my point is that it may be plausible that really strong AI could solve the cancer problem but that it doesn't matter.
The point that both AI and cancer are much harder and much different problem than even the optimistic researchers in the fields imagine (why they're still optimistic).
Most of the time cancer cure articles are met here by someone who posts a link describing how two side of even a single tumor will often involve substantially different cells with substantially dynamics. And each of these dynamics is a real challenge to the human (and the challenge varies because each person physiology varies more than is common recognized) . A strong enough AI could be sending drugs separately to each side of the tumor, yes. But the AI would have to figuring out the dynamics of those particular cells. And I mean those particular cells, not the other cells kind of like them in some laboratory (yes, the presenter deals with this issue but I claim it's harder, much harder than he claims).
Basically, there is no AI of sufficient quality to have the flexibility to figure out each person's cancer. There's nothing flexible enough in theory so there's nothing to apply. Modern AI can recognize a lot of patterns and can use fixed rules to solve problems but it's far from the human ability to put all these things together. And our human ability here is, itself, not up to the challenge. You can have a fifty experts treating a single person's cancer and the chance of success won't go that much, etc.
 See: http://www.anapsid.org/aboutmk/biochem.html etc
1) The search space is practically infinite dimensional. All methods suck when trying to extract a causative model from an infinite search space. There's a reason why in experimental design we change as little as possible.
2) SNP's are not the entire story. If it were this simple we would have progressed much further already. See dismal failure of all other high throughput sequencing and microarray technology. We still don't know how to analyse this stuff properly, if it will ever be possible.
3) The metabolome is adaptive! While we each have different enzyme kinetics due to slight differences in protein makeup, overall metabolic flux rates are amazingly consistent. See Oliver Feihn et al for more details.
To answer your second question, cancer is generally accepted as a genetic disease ie mutations, copy number alterations, insertion and deletion of genetic information, however, recent research has shown that epigenetic processes (that is what your cells are doing with your genes such as alternative splicing or DNA methylation) are also an important factor and these can be effected by environmental factors such as diet, exercise, even mood.
Yeah, patients relapsing into cancer usually do not have much alternatives. Combination therapies often help since they can attach several pathways at once, but combo therapies are usually limited to 2 compounds at the same time.
Another huge problem is linked to medical practice. So many doctors treating cancer patients are just NOT aware of the latest studies and developments in terms of Standards of Care. If you have a cancer, the most relevant factor is the necessarily the drug you take but who's treating you and how much he knows about your condition.
Helping doctors make decisions may be another area for disruption, where Software may help.
Check out this gene therapy called Gendicine approved in China to reverse cancer.
Apparently, the treatment has been available for years, and yet the product has failed to penetrate to the U.S. It would be funny if it were not true.