There has to be some limit for the company. Let's forget a minute about big evil corporation and take a little local company that hire a new person that is needed to run the shop. If this person is absent unlimited and you don't have the funds to hire a replacement, should you just close the shop? It doesn't mean we can put an arbitrary limit on sickness but rather than at some point the company have the liberty to let you go if you can't fulfil your part of the contract anymore in the forsable future. It doesn't mean there shouldn't be a system to help the sick person recover, but maybe that's not the company's job past a certain time, and rather the role of social/health insurance.
Here in Sweden your workplace will pay 80% of your salary for the first 7 days, and then if you are still sick, you need to get a doctor's note and then the state will pay you instead.
Also if your kid is sick you can be home with 80% salary paid by the state.
Yeah, this is why in many countries, Australia included, part of parental leave is paid by the state (it's at minimum wage, which isn't super high, but much higher than other countrie), and the company isn't required to pay anything extra (but must let you take leave).
Most employers however, are much more generous than this to attract talent.
Where I've worked you'd hit a limit after a certain number of consecutive sick days and then move on the a short or long term disability package which wouldn't be at full pay but not ruinous either. I'm not sure those are usable to care for somebody else though