I live and work in the US. If we're sick, its taken from our holiday days... Needless to say people rarely take them, and if they have a bit of a headache or cold, they just come in.
Bafflingly backward, is America.
Not all employers in America are that bad. I work for a tech company and we have a great sick leave policy. You can have up to six months full pay and six months half pay, and take it whenever you like. You require a doctor's note for an absence longer than a week, if I recall correctly. Sick leave is treated separately to your annual vacation accrual.
Whilst many states in America (including California) do have employment law that defines employment as being "at will", meaning that for most non-executive jobs, you can be fired (or leave) at any time, for any reason, I believe that this can actually lead to
better work output. I find that people who work at my employer, actually want to be there. They could walk out at any point, but they stay because they want to be there. The same is for the company. People are employed by the company because the employer wants them there.
This "at-will" law can be abused by bad employers, sure, but if you're a skilled worker and work for a good employer, I think that you will find that the at-will employment clause doesn't have very much, if any, bearing on your day-to-day job. The standard notice period in my company is 2 weeks, and it's entirely customary. You could walk out at any time if you so desired. My employer (still) pays very generous severance packages, on the odd occasion when people do get made redundant (which is rare), and these far exceed the statutory redundancy payment defined in UK employment law, even for the lowest ranking job. I know one guy who got made redundant a few years ago who told me that he was happy that he had been made redundant, because his severance check was large enough for him to not have to work for at least a year, if not two. He was in his 30s.
I think that the idea of a "job for life" can lead to poor workforce outcomes, as seen by various stories just on this forum! Public sector jobs are especially bad for this, both in America as well as the UK. At my company, your work output is all that really matters. This means that no one minds when you come in or leave, as long as you make any mandatory commitments, like meetings, which can mostly be taken from anywhere, even a beach in Hawaii.