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.