I share your shock, and try to keep myself from feeling that the current situation in the US is either normal or ethical. To answer your question, yes, recovery from cancer would could from the pool of sick days in most places in the US. If the recovery takes more than the pool of sick days (7-9 days per year, somehow and perversely being different on average by seniority[0]), then all remaining recovery time is unpaid.
Sick days are meant to be used for recovery from minor illness, not for cancer. This is why short- and long-term disability insurance exist, which pay your full salary or close to it. For example my employer pays for everyone to have ST and LT coverage up to 60 or 80% of salary (I forget which honestly) and you can purchase additional coverage which is (I think) pretax to bring that up to 100% for one or both. For example I have the partial coverage for ST but pay something like $15/mo for 100% on the LT if something were to happen to me requiring extended care. And every job I've ever had from six-figure consultant to $6.15/hr dishwasher has offered STD/LTD insurance (of varying quality, of course).
It's not nearly as barbaric as you're making it sound if you actually understand how it's supposed to used.
Only 20% of service workers have disability insurance, and I don't know of any fast food franchisee or hotel franchisee or pretty much any other small business that offers disability insurance. I would say it's still pretty barbaric. The lower your pay, the lower your benefits.
At least for any job I've had in the US (middle class), one of your benefits is disability insurance (which the employer usually covers 100% of premiums) which pays you 60% of your salary if you can't work.
Only 1/3rd of non government employees have short term disability insurance. If you're a white collar office employee, you maybe have a 50% chance of having short term disability insurance, with the higher you get paid, the more likely you have it.
But for the people that need it the most, lower paid service workers, only 20% have it.
