This is not actually necessarily true at all, at least not in a useful way. Even if it happens to be true, "with enough data" is a hell of a qualifier for many things, never mind one that involves practicing medicine on real patients.

I can't help but suspect that the brilliant success of machine learning in some tasks with a ludicrous amount of data available has blinded us a bit. "Just use more data" is a seductively easy answer to all questions if we ignore any and all factors beyond what is theoretically possible in the 'true Turing machine on a perfectly flat friction-less plane...' sense.

Mammograms are used for preliminary screening. They are cheap, relatively easy to perform, and close to as (physically) noninvasive as you can get for something reasonably called a test.

So immediately most data is simply unavailable without obviating the entire point of doing better preliminary screening. Any data we can consider without making the entire endeavor pointless will be extraordinarily challenging to work with. Even if you use the magic hand-wave to move few 'little' fields like probably most all of NLP into the realm of the trivial, this is an extremely challenging problem. Even if you can magically encode the entire medical history, you'd have what, a massively sparse set of massively sparse time series? And lots of information is going to be in the relationships of different time series, but also you have to deal with doctors not being a single immutable entity... and doctors can only see so many patients in a day, and they only work so many years, and and andandand...

So many difficulties, so many confounding problems, and so little data to brute force the solution.

And if we somehow rally the world to our cause and somehow throw enough resources at it to amazingly solve all the problems... what do we do for the world? Let's use the best imaginable case. The new test is perfectly accurate, specific, and sensitive. It is instant, risk-free, and otherwise just free in all ways you can imagine, to the point that all breast cancer is now detected at the literal possible earliest moment. Not only that, we can do way better. We can even determine if it should be treated or not.

Almost 13% of women in the US will get invasive breast cancer in their lifetime, but only 2.6% die of it [0]. We can spare that 10% or so of dreadful side effects from chemo, radiation, major surgery, and all that. Just to put the icing on the impossibly-large cake, we can even suggest optimal treatments, so that none of those 2.6% die from treatment. We have effectively eradicated death by breast cancer in any way.

Of course, this would (very seriously) be extraordinarily great. I don't even have the words, so I'll just leave it.

This is best case scenario. Everything is impossibly perfect. We're probably at least a couple dozen plausible-actual-miracles deep. So how does this stack up? Well... 2.6% probably clued you in. Breast cancer is not a particularly huge cause of death. From [1] (if you forgive the year gap), we're looking at something on the scale of diabetes (2.7%). We're well below death by unintentional injury (4.4%). Heart attack (21.8%) and all cancer (20.7%) are the two major ones. But breast cancer, well, isn't the only cancer.

But the other side of the coin is that we expanded preliminary screening to young folks. So maybe if we save a lot of them, we've added more human-years-lived than it seems from total death rates.

Well... no. Mammograms are used later in life for a reason. Younger folks aren't very likely at all to have invasive breast cancer. At 20, 0.1% of women get it, and 0.055% die of it. At 40 (the age suggested in [0] to start offering mammograms) it's 1.5%/0.2%. You get the idea.

Maybe for some age it's at least a significant cause of death? Nope. [1] has a breakdown by age.

So frankly... absolute impossible best-case we mostly prolong the lives of a few percent of the oldest women. Large numbers obviously means there's more than a just a few younger women too, but the distribution of possible beneficiaries is rather skewed towards the oldest.

Still. It'd be unfathomably awesome to see for many reasons - both technical and humanitarian. But the degree of difficulty is extreme and the far, far upper bound isn't quite proportional. There's easier targets with better rewards. My random speculation from thinking about this for way too long to write this is that solving many of those huge challenges along the way would probably be the bigger boon for humanity in the end.

TL;DR (yes it's still long, but relative, okay?)
* Preliminary screens need to be simple and non-invasive means way little data, means just throwing machine learning at it very hard
* Many very hard problems means maybe tons of data is needed to push through with sheer weight of data, but human interactions can only generate so much data so fast
* Not that many people of any age get breast cancer, and far fewer actually die of it
* And the age distribution of those who get it skews substantially older... hence the entire reason for mammograms not being used on young folk in the first place... and hence this entirely way too long response to a rather short and probably not-much-thought-of comment

[0] https://www.cancer.org/content/dam/cancer-org/research/cance...
[1] https://www.cdc.gov/women/lcod/2017/all-races-origins/index....