The US has poor employee regulations though, most other well developed nations have figured out people being sick at work doesn't help.

In Australia, full-time employees (38 hours or more a week) will grant you 10 sick days a year. You can use this at effectively any time (Some employers may request medical certificates for consecutive days) but when using it, you are paid your full normal rate for the hours you are away from work for. Once you run out of sick leave, you can then use "unpaid sick leave", which is exactly what you expect.

https://www.fairwork.gov.au/leave/sick-and-carers-leave