That being said, there are a number of reasons that I believe it's so prevalent.
(1) 5 year long survival studies are long and risky affairs, increasing that number just makes it longer and riskier
(2) particularly when speaking about differences in treatment, a statistically significant average increase of 1 month survival over standard of care is sufficient to supplant it, so OS5 v. OS10 doesn't change much if your treating advanced cancers that result in deaths before 5 years.
When it comes to most cancers though, I think OS5 is a very bad stat.
Cancer tends to (though not always) correlate with age when you break it up by type of cancer. For example, children don't get prostate cancer or lung cancer all that often. Similarly, Retinoblastoma and other types of cancer are more common amongst children. So, because of that, you have a built-in tendency to control for age and allow the 5-year statistic to be more of a valid comparison. Similarly, you can calculate 5 year survival rates for any set of subgroups you want – break it up by age, race, gender, co-morbidity or even cancer variant (many of those are frequently done) and then compare. At some point (usually in pretty quickly) the 5 year survival rate is a meaningful comparison...
Also, to be honest/in my opinion, 5 years is a meaningful number for the lived experience. You can imagine doing a lot in five years vs, say, 6 months – so for that reason, it's a useful metric for generally understanding "what chance do I have at having more life to truly live?"
5-year survival is just one measure of health. You proposed two others, but none of them are the complete picture. They're all about the same really. Best is actually looking at the distribution of each metric you care about, but then those curves are hard to compare.
Breast cancer mostly affects women 45+ -- or younger women with a genetic disposition.
Maybe even greater is the opportunity cost. If you have a good result, it would take the double of time for the society to benefit from it.
When you look at medicine as a business based on billing all the needs justifications make so much more sense.
Also, why has the threshold for high blood pressure moved lower over the last 20 years (multiple times)?