I agree with you. Unfortunately, like Wade has said, our society values pushing through and being at work and the like more than our general (or collective) well-being.
If I were to ask my company for a sick day with no impact to work, they'd say yes.
If I were to ask my company for a sick day and impact my work, they'd say no.
The reason I am at work is to make my company money. They don't care about employee well being, unless it means that it'd hurt productivity. And then, they'd find someone else to do the work, leaving said employee without work. At least, this is how it is at my current company and previous two companies.
Should it be this way? No.
Is it this way? Yes.
And starting to rant now.....
IMO, it's one reason that companies are going to start struggling with my generation and those younger. Companies want to keep it status quo, no one retiring, no one moving, and everything quite stagnant--well, except for requiring profits to increase. They decrease the amount of time required to do work, increase the workload, and remove pertinent items that allow us to do our jobs because it reduces overhead costs.* The problem they're going to face, and are starting to face, is that my generation and those younger aren't going to put up with the status quo for the sake of having a job. The "American dream" isn't real for my generation; we're being swallowed up by debt from education that's pretty much now the standard requirement, not able to afford or able to obtain mortgages, and frankly, we care more about job satisfaction than making someone else money.
Stopping now before I go on and on...
*On a somewhat related topic, having open office layouts only work if they're going to pay and provide the amenities that companies like Google, Apple, Amazon, etc. provide their employees. Otherwise, it just causes people to get on each others' nerves.